Any non-polar solvent (anything not water soluble) should work. I use rubbing alcohol, 70% if I can get it. I use that for both my tools and my hands. I find that if I get the propolis softened up with the rubbing alcohol and then wash my hands with dish soap, NOT hand soap, I'm clean enough to go about the rest of my business without making everything sticky. Sometimes my hands, particularly the cracks around my nails, will be stained for a few days, but that's no big deal.
Speaking of chewing gum, I actually tried chewing propolis like chewing gum the other day, because I've heard of people doing that. Propolis is extremely good for your teeth. It was fine, but it was kind of bitter tasting, and if I chewed on it too hard it would get too stuck in my teeth to be any fun.