Use NuShield if you're worried about messing up anything. If you don't want to do that and are actually good about cleaning, they sell anti-static and lint free cleaning thingies for monitors. I have one but it is shaped like a little stuffed pig, it is a duster, I assume you could purchase a box of wipes (usually 100 per box) - those are less gay.
P.S. That Magic Eraser you see on TV removes crayon marks from anywhere. You should get one if you have a crayola-happy kid.
If you happened to score a wife with the kid, ask her for a make-up application wedge (or make-up dohickey, as most girls call them) and you can use that on your monitor.