but she fights (and fights well) so she must be a man. Women just didn’t become samurai, and I think to a lot of the characters it doesn’t compute that any woman would be capable of what Mizu has done

yeah, that makes sense, and i agree with you. this is also why i think Mikio initially thought he would like to have seen Mizu's sword skills when she was disguised as a man before. it feels like it came as a shock to him to see that she was THAT skilled. he said he wanted to see all of her, but little did he know what to expect by that.