I woul actually encourage doing Frank Sinatra songs for this audition, so that you can demonstrate that you can put them over. Check out Rodgers and Hart in particular--"Lady is a Tramp", "Witchcraft" (that's Cy Coleman), "Sunny Side of the Street", "I've Got You Under My Skin", "I've Got the World on a String", "Chicago, Chicago" for uptempo, and "One for My Baby", "Bewitched", "I Could Write a Book", and "Young at Heart" for ballads. Don't imitate Sinatra, though--just show you can handle this style.
I ask in all honesty/What would life be?/Without a song and a dance, what are we?/So I say "Thank you for the music/For giving it to me."