I'm thinking more along the lines of Big Jim now. And that's scary. But I've been persuaded into thinking that there really is no such thing as an uncoverable song. So while I was showering (when most inspiration hits) I thought of these songs that may be challenging, even though I'm sure they've been covered:
He works hard for the money - Donna Summer
You make me feel like dancin' - Leo Sayer
When you wish upon a star - Jiminey Cricket (aka, Cliff Edwards)
I did it my way - Frank Sinatra's famous song

or a real classic that needs to be done better:
Midnight at the oasis - Maria Muldauer