I’m with Lister in forcing a different direction. I usually pull out some different music to play, usually something far from my standard: my mom’s Beethoven, Sinatra, something written for a different instrument.
At our former blues jam, we had a Q/A session where one of the questions was, "Who is balder, Yule Brynner, or Telly Savalas?"
There was a brief pause, and then someone's old grandma piped up, "Both!"
Which is somewhat unusual, considering the brouhaha amidst the grandparents, their kids, their grandkids, and just about all walks of life listening in. When the usual fare wasn't causing finger or toe-tapping, the host guitarist would do his best Marilyn Monroe's voice and sing Happy Birthday to some unsuspecting attendee.
We'd laugh but the host could only do that once per week since it messed up his voice pretty badly.
We also did the shave and a haircut soundbite, the Henry Mancini Peter Gunn theme, and the Sanford & Son theme song when the waitresses would collect the used dishes and glasses towards the end of the evening...the are several others I can't quite remember, but if your cover band needs new material, try copping a few TV show or notable theme songs folks will identify with.