I think there are plenty of songs originally sung by a female character that can be gender neutral ("Nobody's on Nobody's Side", "Defying Gravity" for example.)
However, when I sing, say "Defying Gravity" I raise it 4 keys so that it's in my "belting" range (when its in the original key and you sing it in your natural voice, not your falsetto, it's not as powerful)
So I think the key is finding a song, adjusting the key so its in a correct key for your voice, then if you want see if there is some altered lyrics (changing "Him" to "her and such) OR keep the lyrics the same.
"Life in theater is give and take...but you need to be ready to give more then you take..."