Well, not trying to collect unrelated martial arts like some kind of overly aggressive Pokemon trainer comes to mind.
Situations like this are what tactical batons and pistols are made for. A hitman is not the kind of person that’s going to be blindsided by random street thugs, no matter how awesome said thugs think they are.
A hitman is someone who, by definition, understands how fragile people are, and one that was smart enough to survive a career in that field is not going to be dumb enough to get into an unarmed brawl with shifty looking guys.
They need to have a functional grasp of threat assessment. That means knowing where someone’s likely to ambush you and not walking into that.
They need to understand that any fight they do find themselves in needs to be over as quickly as possible. That means using whatever tools are at their disposal. Fundamentally assuming your character will be mixing multiple martial arts styles together to deal with a couple opponents is missing the point. Your character has chosen to descend to their level for no legitimate reason, and it will get them killed.
Your hitman was learning skills necessary for them to do their job, that didn’t include hand to hand because the kind of exposure hand to hand kills require wouldn’t allow them to finish their career outside of a prison cell.
So, we’re back to, he’d just kill them, and move on with his day. No complex choreographed fifteen minute fight, he’d waste them, avoid them, or bait them into getting arrested. Things that wouldn’t put him in any more jeopardy.
I know our spies and assassin recommendation list varies a little, but here’s some relevant suggestions:
Ronin (1998): The characters are technically spies turned mercenary, but a lot of the basic advice, and outlook, is in line for a retired assassin.
Collateral (2004): Michael Mann’s crime films, in general, are pretty good about getting the right outlook, but Vincent (Tom Cruise) does an excellent job of presenting the kind of could, almost reptilian, view of the world you need to kill people for a living, while also demonstrating a shocking degree of competence in protecting himself, while still getting the job done.
Heat (1995): Somewhere between the two above examples. It’s a Michael Mann film with Robert De Niro. Again, this one isn’t about assassins per say, but it is about professional criminals, which is ultimately, what you’re talking about. Your character just used to kill people, instead of robbing banks.
With both Mann films, I really recommend watching them with the commentary on. There’s a real wealth of information on criminal psychology on there.