Well, thanks for the recommendations!
I picked up a box of Nitrile gloves from CVS across the street.
They worked great. I was worried that they would tear and not be strong enough for the task, but they held up just fine. We never even opened the container of Handi-wipes I got. Jim, the guy leading the talk, had a HUGE cask of GoJo, but we never even used it. Well, maybe he did. He didn't wear the gloves and his hands were filthy!