Hm I don't see why not! As you said many other songs have this done (sometimes the changed version is known even more than the original) so it wouldn't be the first time. As long as you don't change any of the other lyrics.
I think it's less common today because a lot of performers aren't so uncomfortable singing a song written for say a man to sing to or about a woman ("her") if they're a woman, but this is a different situation because the song is actually supposed to be about the singer so it really would be strange to sing about a female if you're a man.
It's a great song (especially Simone's somber quodlibet version) so you go at it!
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