Uh....that was Cher who sang “Bang Bang”.
But she’s yet another aging wealthy leftwing hypocrite, so no big deal.
Sinatra had it on her album “How Does That Grab You”
in ‘66. But your right. Sinatra, Cher both need to
go to Jupiter.
Nancy Sinatra also covered Bang Bang - kinda of a slow & melancholy version...and much better than Cher’s.
Also used in the film, “Kill Bill”
https://www.youtube.com/watch?v=U2LAdyE8lEU