Realistically? She won’t kill him, her guards will. (She won’t even get close to him and his challenge is meaningless.)
This is the most important thing to remember: a female noble heir is the social and economic future of their household, if your pirate captain takes her then he gets to claim her which is the equivalent of stealing Alabama, Alaska, or California. Now do you think for a second her guards or her family will allow that to happen? (The answer is no.)
If you’re using pirates, then you’re probably pulling from the Golden Age of Piracy for inspiration, so between 1650 and 1726. It’s important to remember than aristocrats in any period before the 19th century were not decorative. Today, we (Americans especially) have a habit of confusing the echoes for the gunfire. We view the nobility and royalty like CEOs and other really rich people instead of what they really were: warlords, an important part of their nation’s command and control structure. Nobles were taught to fight because they needed to be capable of defending themselves from the peasantry, from other nobles, and from attempts at political assassination. Your heir is probably living in a period where she is expected to know how to fight because someone else is going to try to kill or kidnap her. While we’re talking about a period in history where the importance of the nobility was ending, it wasn’t there yet. Fencing as recreation hadn’t quite taken hold yet and your heir’s education is going to be for realities of the world she’ll be facing. This is also a period in history when training with live blades was not uncommon.
Nobles engaged professional swordmasters as members of their households to teach them and their children. Your girl is likely to have had a fencing blade in her hand by the time she was six years old, the standard training age for an aristocrat. It’s likely she was trained on a variety of weapons, but depending on your time period her main sword is likely to be either a rapier, an epee or another variant of smallsword, all of which will turn your pirate captain into Swiss cheese before he can say “what’s that?”. She’ll possibly also know how to use a longsword (still saw battlefield use) or a heavy saber (as opposed to the later lighter version of the fencing blade) as a cavalry blade, she’ll have been trained to use it from horseback in case she was ever called to military service by her monarch. If her family employs a professional duelist to fight for her father or mother in case of another noble challenging the family, she might have also trained with them. If her family doesn’t have the money or the family patriarch prefers to handle to duels themselves, it’s likely she was grilled by them regularly. As the heir, she’ll be under direct scrutiny from whichever figure is managing her education and training to ensure she can do her job when she eventually inherits management of the household/estate.
The problem here is that you’re thinking about this in terms of her not having any practical combat experience and conflating the 18th and 19th century nobility with the 16th and 17th century is a terrible, if common, mistake. Unless your pirate captain is a former member of the gentlemen class or noble class then the weapon he’ll be using is likely to be the cutlass, which while a fantastic weapon for boarding actions, is horribly outmatched by both the epee and the rapier when it comes to dueling. They’re both longer (reach and speed advantage) and faster (substantial speed advantage) and in the hands of someone who knows how to kill with them. Weapons are a great equalizer, your heir doesn’t need to be exceptional to kill him, she’ll be armed with the better weapon for the situation and has the knowledge to know how to use it in practical combat. Even if she’s armed with a longsword, she’ll win.
Here’s your first real issue: you’re conflating all types of combat experience together while ignoring the separate skill sets and types of experience. A pirate captain is going to be experienced in ship to ship combat and boarding actions, his exceptional talent is the handling of his crew and his ability to command. This is what he needs to be good at in order to maintain his position. Dueling is not going to be his focus, he may excel at dueling other pirates both with pistols and with swords but the question is who is he dueling? The caliber of your opponent does a lot to enhance skill, so does having the luxury to devote the necessary time to developing that skill. A boarding action is a mass melee, it’s not a duel. Even if he’s used to fighting multiple enemies, it’s going to be in fighting back to back with the support of his crew. His most common opponents are going to be other pirates, most likely drunk pirates, while on shore leave. This doesn’t leave him a lot of time to come up with the skill necessary to hand a noble their ass in a one on one. A duel with your heir is going to end up looking a lot like Edmond Dantes’ first duel with Ferdinand in The Count of Monte Cristo (2002). Your pirate is Dantes, she’s Ferdinand and she’s got less reason to play nice. (It’s worth noting Ferdinand isn’t even considered an exceptional duelist and, at this point in the movie, he’s just got the advantage of his training.)
Now, he could be a former naval officer or son of a merchant with a business in overseas trade. However, this would mean he comes from either a wealthy merchant family or the middle/upper class. At this point in history officers were still expected to buy their commissions which meant ships were largely commanded by the rich/gentlemen and the sailors/grunts were pulled from the poor/uneducated.
The second issue: Heirs are incredibly valuable, incredibly valuable. Female ones especially because they are the means of carrying on your bloodline. A lot of effort and work by the head of the household goes into the heir because they are the economic and socio-political future of the family. Heirs are not allowed to engage in the same sort of risky business that a second or third child can get away with. A fairly decent modern comparison is Prince William versus Prince Harry, both are in the military but only one gets to fight on the front lines. Now, you can disinherit the heir to ensure that their progeny/new husband cannot claim their titles and lands but you lose all the effort that went into them in favor of (what is likely to be viewed as) a substandard second aka the spare. So, again, it would be like stealing Alabama and she doesn’t have the free time to run off for a weekend cruise with a strange man unless she’s intending to throw away everything anyway (and no one is going to let her).
Second to the Family Head, the Heir is the most well-defended member of the family. They’re not getting out of the house without an escort, these men (and women) will be among the most loyal and skilled men (and women) the house has at their disposal. She’s not going to go anywhere without them and has probably known them (somewhere between four to six) all her life. They may know her better than her parents do, they’re always there, and they will defend her with their lives. Not being a noble, your captain has no ability to challenge her directly even if she challenges him. He is going to have to go through them to fight her and they aren’t going to bother with a duel. They’re not going to fight him one on one, they’ll fight him together. He’s outnumbered and fighting better trained opponents (it’s going to be either three on one with one guarding the girl or four on one with two guarding the girl), so he’s dead.
It’s important to remember that a bodyguard’s job is not to do what their protectee wants, it’s to do what is best for them and ensures their safety. It’s their job to keep them alive, not to keep them happy. She’s not the one paying their salary, her parents are, and even if she was it wouldn’t make a difference. While her guards are fighting him, the other one (or two) will hustle her somewhere else to keep her safe.
Third Problem: In attempting to take her anywhere, he has shown he means her harm. Whether it’s to kill her, ransom her, or claim her as his wife is irrelevant, whether he actually intends any of those things is irrelevant. From her perspective, that of her family, and her guards, he intends her harm and if she’s forced to fight him then it will be to the death. Remember, these are threats she faces from the other members of her country’s nobility. She’s primed to respond to any threats to her person with deadly force and so are her guards, all of whom are likely to face much more talented combatants from their own class than the pirate captain. She has a vested interest in being better at combat than him and she will be because nobles are not sheltered fragile flowers who have the luxury of using money instead of force to protect themselves. The French Revolution was successful because of the number of peasants and the willingness to bury the aristocrats in bodies (which was what it took). It wasn’t because they were better warriors.
Do Not Steal California: Heirs are valuable and important people, stealing them is a lot like stealing the ownership of a state. Lots of people are bound to try it and there are reasons their families take steps to ensure they won’t succeed.
A Rapier or Epee versus a Cutlass: both weapons have a reach advantage over a cutlass and are much, much faster. The pirate captain’s brain will not be used to fighting at it’s speeds and in a single unarmored bout, it will be over in one or two hits. In fact, historically the epee is so fast that it resulted in multiple double suicides during duels which is part of the reason we switched to fencing with blunted blades.
Nobles Are Not Decorative: Unless we’re discussing nobles in the 19th (excluding Russia), 20th, and 21st centuries then an aristocrat’s position was fraught with danger. Even in the 18th century when they were heading toward being obsolete, nobles were very dangerous individuals who faced a great deal of danger in their everyday lives both from the peasantry and members of their own class.
Depending on Context All Combat Experience Is Not Created Equal: while there were pirates who were very skilled duelists this was usually a skill they cultivated during the time before they became pirates (as members of the gentry). Pirate Captains needed to be skilled in naval combat, interpersonal skills, leadership, and other skills relating to raiding, theft, and seafaring leaving little time to focus on skills unnecessary to their general lifestyle.
Where the Heir Goes, The Guards Follow or Lead: A noble’s guards are never far away, they travel in packs and it’s their job to defend their master from harm. Getting through them to the protectee isn’t easy and the protectee is unlikely to thank you if you do.
Swords are made for killing: intentions are great, but swords are made for killing. The better the opponent, the less likely the option of not killing. With faster weapons, it becomes very easy to kill accidentally or a wound may become infected leading to death.
Think Leia, Not Gossip Girl: I didn’t actually throw this one out there in the above, but personality wise, you’re better off looking at Princess Leia (especially Leia from A New Hope) as opposed to modern day rich girls like Blaire Waldorf and Serena Vanderwoodsen. Think about Leia’s response to Han and Luke’s rescue attempt on the Death Star, particularly the part where she takes charge and shoots the Stormtroopers. Feisty yes, but also intelligent and capable of taking care of herself. They provide her with the opportunity to escape, but she’s more than able to act for herself when the moment comes and patient enough withstand the indignities and torture inflicted on her by Vader and Tarkin to wait it for it. She’s also all business once she gets out and is much better at providing direction than the boys are at finding it.
In short, he’s dead.
A solution: as fun as the concept of the Princess and the Pirate is most of your problems could be solved by removing the heir part from the equation. If writing a lazy layabout who isn’t interested in real work is your angle with this character then it’s best to go with a member of the family who has the unfortunate luxury of being a strain on finances simply by virtue of their birth. The third child or a bastard the Father/Mother/Family Head refuses to get rid of who gets all the privileges, none of the responsibility, and who the family doesn’t care enough about to take an active interest in their protection or their training will have a much better shot of doing what you want without all the messy complications. They also have a much, much better shot of being in a place where they and the pirate will actually cross paths. Younger children have a much higher likelihood of leaving the country to seek their fortunes or being in less savory places. (Do not have the pirate break into their house, homefield advantage is huge and estates/castles are designed to be deathtraps for invaders. Don’t do it, you can’t have a fight there without drawing twenty or more guards.)
A solution to the sword problem: they’re drunk. Your character is at a low point in their life, they’re in a bar feeling their failure, and they’re drunk when they challenge the pirate. This gives the pirate the luxury to feel sorry for them, you can subtly handicap their actual skill level, and give them the opportunity to grow as a person and a combatant without jeopardizing all the advantages a noble has access to.
Some Reading Suggestions/Historical Figures:
Julie La Maupin: The life of Julie La Maupin could quite literally fill any swashbuckling novel to rival the tales of Alexandre Dumas, her stories however have the advantage of being real. This brash, deadly, bisexual cross-dressing swashbuckler bucked the times and society to carve her own way in 1600s France.
Gurps: Swashbucklers, Roleplaying In The World of Pirates and Musketeers: The Gurps books tend be great reference material and this one is a great overview of everything you need to write about pirates and swashbucklers. It covers the history surrounding pirates and musketeers, the notable historical figures, the socio-political climates of the times, and pretty much everything else you’re going to need to build your setting.
The Three Musketeers by Alexander Dumas. While not a book about pirates, this novel (and the others by Dumas) will be helpful for getting into the frame of mind to write about swashbucklers and nobles. It gets closer to a period when the nobility was still considered relevant and treats them that way.
The Scarlet Pimpernel by Emma Orczy (1903), the foundation for superhero literature and secret identities, this is the novel that inspired Zorro and subsequently Batman. It follows the adventures of wealthy Sir Percy Blakeney in his adventures rescuing individuals sentenced to death by the guillotine during the Reign of Terror. In England, Percy presents himself as a dim fop to throw off suspicion that he (along with a band of merry friends) is the Scarlet Pimpernel, daring escape artist, master swordsman, and outside the box thinker. If nothing else, it’s a fun adventure novel read.
The Errol Flynn Collection: The Seahawk and Captain Blood especially, but I suggest a general review of the Golden Age Swashbuckling films.
The Mask of Zorro, The Count of Monte Cristo, anything with fight scenes choreographed by Bob Anderson for the spectacular sword work which may give you ideas.
Wikitenaur: pretty much the best resource for historical fighting manuals if you want to go outside modern fencing to get ideas for your fight scenes. You will have to slog through some older language, some of the manuals come with plates and translations. Others don’t.
Get a manual on fencing. Even if you don’t plan to take up fencing yourself, a manual for beginners will be helpful for getting the basic ideas and terminology down.
While I wouldn’t recommend Assassin’s Creed IV: Black Flag for it’s historical accuracy (cringeworthy, especially the way it messes with and reduces the awesomeness of some very incredible historical figures) or it’s combat accuracy (also cringeworthy), it’s ship combat is a lot of fun and may help you get into the right mood for when it comes to the fun side of pirates. This depends if you want to shell out for the price tag. The same is true of Pirates of the Caribbean. Decide what pirate theme you’re going with, compare Jack Sparrow with Peter Blood for reference and do some research into historical figures to help you with your captain. If you’re doing a gender equal setting, feel free to research and export the considerations for male nobility onto your female noble.