I'd play it as a man playing a woman. Sally isn't supposed to be a good singer, and she was said to have a low, husky voice, so the singing wouldn't be an issue, and nothing would have to change in the script, so no unintentional hilarity would ensue.
I don't WANT to live in what they call "a certain way." In the first place I'd be no good at it and besides that I don't want to be identified with any one class of people. I want to live every whichway, among all kinds---and know them---and understand them---and love them---THAT's what I want! - Philip Barry (Holiday)