Should be safe as long as there is no other contamination present. The popular rain domes produce simulated rain by concentrating mister output directed at the top screen.
I have not heard of nor had any personal problem running a dripper thru the screen
I used to make drippers with air-valve flow rate adjusters and aquarium air line tubing. Usually they are plastic, not metal so no rust worries at all. Just drill a little hole in a plastic container (such as a plastic gallon jar from walmart) insert the air valve, silicone seal around it, add the length of tubing you desire and you are good to go. If you want to run multiple cages off the same resevoir, just add some splitters or multi-valves to the tubing along the way. All of these parts are simply plastic and easy to install as you know if you are into aquariums.
Sorry for not responding for awhile. I went and got the air flow adjusters and am very happy with how it works. So far no problems with it and the chameleons likes it too.