He's not much of a mechanic,then. Take two sticks,or two leaves,or two pieces of paper,or whatever you find laying around. Using one object,push the rear derailleur forward to slack the chain. Using the second object,lift the chain up and maneuver it onto the closest ring or cog. Then just lift the rear of the bike and spin the cranks to reseat the chain. Nothing get son your hands.

In the future,carry a set of latex/non-latex gloves to keep your hands clean. I also carry a little 1oz squirt bottle from REI that I filled with GoJo hand cleaner and wrapped with paper towels.