Also, something you, Chromolume, are sure to know being a musician is that GENERALLY (note I am not claiming it's absolute) musical theatre songs for women are written on a lower place on the staff than for men. The thrilling top notes are often B's, C's and D's. For men the thrill notes are E's, F's, and G's, etc. For example say a man sings On My Own an octave down. The highest note is a C, which may sound like belt-o-rama for a women, but is going to be pretty tame for a male voice. And I think the reverse is true is a woman sings a man's song an octave up. Imagine the ear bleeding screech fest you'd get if a woman did Why God Why? like that.
My point is, if you are going to gender bend you might have to spend extra time and money to have the song transposed to a key that shows off your instrument.
(sorry for the Boublil and Schonberg references, I used to sing these songs back in the day. I am a man with a really low voice so the women songs always sounded great on me an octave down while I didn't have the high notes to sing the men songs. Career over. LOL)