If I've learned anything in all these years of playing, it's not what you do, as much as HOW you do something. If you play a request, even a skeleton version, they feel like you tried. The nature of this type of show suggests a certain repertoire that most piano guys know, or can at least fake a verse or two. It's bar room sing a long stuff - Sweet Caroline, Brown Eyed Girl, Buttercup, Twist and Shout ... etc. Each player takes a lead, and the other supports him. It's high energy, but you only sing every other song, so you get a break every 4-5 minutes to prepare for your next selection.
Fran's right - I can fake most things, as long as I'm singing the right words, and singing is my strength, so ... the piano is just a backing rhythm. Use ii V I chords and you always find your way home!