There are some female members of the 'rat pack'. Only one is a singer though. But the type of song will still be tough for her. I wonder if somone will do 'somewhere over the rainbow'? Adam perhaps? I would think he'd go for Sinatra though.
From Wiki:
it was the name used by the press and the general public to refer to a group that called itself "the summit" or "the clan," featuring
Frank Sinatra,
Dean Martin,
Sammy Davis, Jr.,
Peter Lawford and
Joey Bishop, who appeared together on stage and in films in the early-1960s, including the movie
Ocean's Eleven.
[1] Despite its reputation as a masculine group, the Rat Pack did have female participants, including movie icons
Shirley MacLaine,
Lauren Bacall,
Angie Dickinson,
Marilyn Monroe, and
Judy Garland