I love I Can Cook Too, though it can be a bitch to get those lyrics down and spit them out. The other catch is relying on an accompanist who can pull it off. Some other ideas:
Hostess With the Mostess - Call Me Madam
Tom, Dick or Harry - Kiss Me, Kate
You Can't Brush Me Off - Louisiana Purchase
What's Going On Here? - Paint Your Wagon
It's Me - Me and Juliet
Shopping Around - Wish You Were Here
The Beast in You - Goldilocks
It's a Helluva Way to Run a Love Affair - Plain and Fancy
Give It All You Got - Oh, Captain!
I Enjoy Being a Girl - Flower Drum Song
I Hate Him - Destry Rides Again
Shy - Once Upon a Mattress
Gentleman Jimmy - Fiorello!
What Did I Ever See in Him? - Bye Bye Birdie
Hey, Look Me Over! - Wildcat
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian