I strongly suspect that neither of your characters are wearing underpants. :D

Modern small, tight underpants is less about reduced prudishness, and more about a)wearing tight clothes that loose ones don't fit under, b) having washing machines that means we can have clean underpants every day, and c) lightweight, highly elastic fabrics that make skintight clothing comfortable and easy to fit.

The main reason the only men's underwear you're finding from that period is long johns is that there was no point in bothering with it if not to keep you warm; too much trouble and discomfort (especially on shipboard!). Your male character probably just tucks the long tails of his shirt around himself to protect his trousers. Your female character, when in skirts, would probably either be wearing no underpants, or bloomers with an open crotch (which is what early women's underpants had; don't want to have to bother taking them off to use the privy); crossdressing, she'd probably either wear nothing or long johns if it's cold (like the men would have), or something improvised to give the impression that she's got a package in her pants.