I just wanted to add, i have tried letting my dripper drip just into my plants. It was a bad idea. Plants can get root rot if to saturated, and gnats love soaking wet soil ( A BIG PEST) that it hard to get rid of. What i used to collect water from my dripper was a little rubber made dish, that i put screen over the top, to keep the chams out.
Also, i have used the same type of cage for baby chameleons. Even with paper towel if you mist correctly it is going to be soaking wet at the end of the day. It will be very important to soak this up every day, or else the air in the cage gets real nasty (bad for cham). It is important to mist you cham for several 5 minutes (at the least) cycle's. Since it can take a cham several minutes to start drinking. I strongly feel that just the water off of the leaves isnt enough, they like to drink the mist as well. Then if they are still thirsty a little bit after the misting they can drink off the leaves. It just seems to me it would be difficult getting your full water fill from the drips on the leaves.
When i was at home watching them or where i could keep an eye on them i would open the door just so they could get some fresh air, since these cages get real stuffy.
I hope this kind of gives you some pointers, I know that these cages can be real frustrating due to stail air, wetness, and keeping it from over heating. An idea for when you buy or build your screen cage, get one or build one with a drain. Just my opinion but it will make a world of difference.