The wet towel seems like it would work to an extent, but you'd have to make sure it didn't block the UVB light. Also, if you have a heat lamp going, you need to make sure you don't create a dangerous situation. What might work better is to attach a damp hand towel or washrag to one of the sides.
Cool mist humidifiers require some cleaning so, in addition to the expense of the machine (not excessive, $20-30) you'll have that, plus it needs to be plugged in and if energy conservation is a thing for you, that's something to consider.