About as realistic as the rest. Most of the time when people talk about “realism” in fiction, they’re butchering the term. In a world where Mayan gods stalk the earth 1500 years after the civilization that worshiped them crumbled to dust, inflicting superpowers on the unwary, it’s not unrealistic at all for you to have a character that’s freakishly accurate with handguns after 300 years of practice, and or mastered several different martial arts. It’s internally consistent, and to an extent, that’s all “realistic” means when we’re talking about fantasy.
What might not be realistic is the idea that he’s alone. That throughout human history, the Mayan gods have never “cursed” others with similar immortality.
Remember, for the nineteenth century, a lot of the modern martial arts didn’t exist, or would have fiercely protected. Your character can’t have learned any Chinese or Japanese forms in that era.
And, while martial arts like Systema have a long history, the modern form is completely different from the historical versions of the form. So, if you really want a martial arts background, you’re going to have to do some research. Also, using the term “martial arts” to refer to unarmed forms is strictly a twentieth century invention.
Really, you’re going to have to decide how much anachronism you’re willing to accept, and then do a lot of research to keep your material appropriate.
some a lot of recommendations:
I’m assuming you’ve already looked at the westerns with quasi supernatural protagonists. If you haven’t, I’d start with Hang ‘Em High, High Plains Drifter, and A Fistful of Dollars. The entire “I thought we killed him” avenging hero is almost it’s own sub-genre in westerns.
Deadlands was a Comedy/Horror/Western RPG in the 90s. The setting is an alternate 1880s American west where the supernatural has broken free and the end of the world may be nigh. It includes an entire mechanic set for playing the classic returned from the grave hero.
Brimestone isn’t a western, but it’s worth looking at (if you can find it). The central character was a cop who died and went to hell in 1983. The show picks up in 1998, there’s been an escape from Hell, and the Devil (played by John Glover) sends him back to earth to hunt down the damned.
Kurosawa’s Yojimbo and the American remake Last Man Standing may seem like odd recommendations, but they’re both worth watching. Neither story is supernatural, but they both deal with a lone fighter clearing a town of two competing gangs.
Millennium is an even stranger recommendation, set in the late 90s, it’s a horror/crime series that deals with a burned out ex-FBI investigator who may, or may not, posses psychic powers. The show has an ongoing supernatural element that is kept very low key until the final season. At it’s core, it’s a story about a man being forced to stand against evil by some supernatural force. Fair warning: each season shifts tone sharply, so it’s effectively three different shows; the first two should be useful for you.
The Dark Tower by Steven King is a series I still need to finish, but what I’ve read of this post apocalyptic/horror/western is good, really good. It might be off tone, but it could be very useful for you, especially in setting up a gunfighter.
The Saint of Killers from Vertigo Comics’ Preacher might be worth looking at. I could do a full article unpacking that comic, but it could be useful if you have the time and resources.
Finally, the Highlander TV series is on point. The original show follows a 400 year old immortal wandering the earth. He doesn’t have a compulsion to get involved, but it should give you some good ideas for how to handle your character. Especially if you want to have him interacting with a cadre of normal characters who follow him.