In my opinion, the shower technique is used in more extreme situations when a chameleon needs hydration, not for added humidity. It is a very temporary thing. There are many ways to add to the humidity of an enclosure, additional misting, plastic on sides, foggers, live plants, etc. This can be more challenging when the animal is free ranged, but it still can be done. Humidity may not be the issue here.
As for stuck shed, the animal will likely take care of it on their own, and unless there is a risk to the chameleon I would just leave it alone. If a risk is present, I would agree with the above mentioned suggestion about the Q-Tip. If there are repeated issues with shedding, I would look to husbandry and see if there is an issue with supplements, lighting or humidity.