If there are no mites visible on it your chameleon doesn't likely have mites...and its very rare for a chameleon to have mites anyhow.
Internal parasites are a different issue. Some can survive the cleaning we do to cages unless you use steam. You will only have to worry about parasites if your chameleon has them...and the only way to find out for sure is to get a fecal done. Most of the parasites that a chameleon can get won't live in a human.