ok so i've watched all of blue eye samurai and i am here to deliver you an analysis as to why i see mizu as a trans guy. to begin with, obviously this is by definition my headcanon, we're all entitled to our opinions, everything is up for interpretation, etc. i'm gonna use they/them pronouns for mizu for the sake of legibility.
but i think i'm right and here's why:
the obvious argument for mizu being a cis woman is that they're living in a heavily patriarchal and misogynistic society in which women are viewed as property. and, on mizu's die-hard revenge quest, obviously dressing as a man is going to make moving about the world easier.
however, there are women in this setting who can move about easily. we know that a widow and her kid need a travel pass and a chaperone, but lady kaji and the other girls move from city to city freely (also, in this period of japan, prostitutes could in fact move around with far more ease than other women in the setting). not to mention that they're shown as the only women with access to Fowler, to any of the white men. mizu's own mother is a whore, they know that the white men buy company all the time. mizu's very existence is proof that there are women who can get close to the white men with no problem.
now, mizu cares about one thing, and it's revenge. and there is a way for mizu to accomplish this revenge without dressing as a man. and they don't take it. like at no point in the whole story do they take it, even for a minute.
but the bounty! you say. mizu can't just dress as a woman, they're looking for a woman with blue eyes!
except, after their marriage to mikai and getting turned in, they aren't. we even hear fowler say that he thought all of the bastards were tracked down when he meets mizu. not one of the characters, even the high-profile ones, who note mizu's eyes mention a bounty out for anyone with blue eyes.
also, even if the bounty was still a concern, uh, mizu can fight. they're no longer in hiding for their mother, and they're well capable of dispatching anyone who recognizes that there's a bounty out for them, or tries to turn them in.
and even then, after being allowed to live as a woman (and live a nice life!) for a year, and freed from their bounty, what does mizu decide to do? go live as a man. the whole entire time. even when completely alone. this guy decides the bandages are staying ON unless it's for bathing or ritual samurai blade purification.
the thing that really got me is sneaking into fowler's island. mizu gets the information that prostitutes are allowed in, and are certainly allowed in frequently enough that they are being purchased their own sake. and i, the viewer, immediately went, "oh, so this will be where mizu physically being a woman will be used to their advantage, since this is a character who will basically do anything to get their revenge. they're gonna put on the heels and fancy robe and go kill some white guy with a hairpin."
nope! instead of taking this very reliable route to their revenge, mizu decides to moonlight as an assassin to get the information required to nearly drown and then fucking fight through nine floors of shit trying to kill them to get to this guy. instead of, like they tease earlier, walking through the front door.
as in, mizu literally chooses to get revenge the Man Way over the Woman Way when the Man Way comes with "likely death" and the woman way comes with, uh, wearing a nice robe and some makeup.
this is a character who isn't a stranger to sex, to quiet kills, to wearing women's shoes, to living as a woman, or to being seen as lesser-than. who doesn't care about anything--not lives, not honor, not being a samurai--when it comes to getting revenge. and yet, the idea of being seen as a woman, of presenting as a woman, even for the sake of that revenge quest is so unthinkable that they don't even consider it.
like, i cannot stress enough, the story gives mizu a silver-platter opportunity to both be a woman AND fulfill their revenge at this point in the story. and mizu basically says "I'd rather die as a man even if that means I don't get my revenge." this is a character who is canonically very intelligent, dedicated, and can fight in heels. who outsmarts trained assassins.
i think that yes, this is feudal japan and modern sexuality labels would not be applied to these characters. however, when a character is born female and chooses to live entirely as a man when they could otherwise accomplish their goals and have a happy life living as a woman, it seems pretty obvious to me that they, you know, identify with being a man when they were assigned female at birth. which would make them a trans man.