ok, as there's been 83 people viewing but only 4 voting, i'll fess up: it's a trick question.
not only doesn't a mensch even have to be a man, cut or otherwise, but a mensch does not even always have to be a mensch. while a schmuck is a guy who pees in the shower "don't pee in the shower, you schmuck!", it could be argued that it is better to be a schmuck than to be a shmegegge "why didn't you just pee in the shower?" and while it's nice to think you're always such a mensch, what mensch hasn't had the urge to pee while in the shower? now if you suffer through your shower without peeing, then, well, and i didn't even know this, but according to masterblaster, you're a schlemazel, out of luck.