Only problem with showering is there are some negative side affects.
For one, it can cause great stress to the chameleon, and I also unfortunately had a 9 month old ambilobe male, that received an eye infection I believe was from showering. His eye infection made him go blind in his eye, and caused more stress. The type of water used when showering isn't filtered or cleaned.
I think a great alternative, is misting 2-3 times per day, or have a mist-kit which mists several times at 40 second intervals throughout the day. This keeps the humidity up, and get him a little wett here and there, but keeps it as natural as possible. Yes it may cause him a little stress... But the water I use from my mist kit is siphoned from a treated water for my chameleons.
Humidity= misting often, plus live plants and watering helps. And a dripper 2
Hope this helps
I live in California, with traces of cocaine and heroin in our water supply ;(. So I cannot go by tap water consumption. ;(