Your veiled being under it is better than nothing. Hand misting is also good. If he looks dehydrated, I use as many ways to get him water as I can. A milk jug is a good dripper. Just poke a tiny hole in it.
I blew through 2 reptifoggers in a month! They work great for about 2 days then start making terrible noises! Get a cheap humidier for sure! I just keep my humidier on low and it keeps his little room at around 50 or 60% (I own a veiled). Your cham will indeed lick drops of water lol that's how they drink 8) they don't use wate bulls and when I used repti foggers it just stressed my little guy out 8l
Here is the humidifier that I use for my veileds, I recommend it to anybody. It's quiet, and it keeps the humidity up and doesn't soak everything.
I also have two Repti-Foggers for both my cages to use as a watering system. I keep them on high to maintain lots of water droplets.