Maybe you could play songs that are harder to sing, like “Take On Me” with that falsetto screech in the chorus.
Follow it up by “Blinded by the Light,” where you know they’ll botch the lyrics nobody can ever make out. “Wrapped up like a dude another rotor on the right…”
Then work in a song completely inappropriate for the singer, so that a burly 300-pound fellow has to belt out “I Feel Pretty,” assuming you’re not in a venue where that would be a normal thing, in which case you pull our your heavy metal fakebook.
Finally, you can play lots of songs that are duets, and hope they don’t have a buddy ready to join in.