Listen to your Barbra. That is her voice. She has recorded an amazing and huge catalog of songs wide ranging in type.
Just do not do He Touched Me since it has been done in every beauty pageant since 1965. Same with Happy Days Are Here Again.
Off the bat, try I'm All Smiles. I think it is on one of three albums called People, My Name is Barbra or My Name is Barbra Two. It was published in the show songbook for a fast flop called The Yearling. Barbra recorded three or four songs from the show as a favor to the composer who was a friend of hers.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher