how do you know whether they are wood mites or not. I ask as I would NOT trust anyones word on that. You do not see mites until it is too late. When they are just hatched out they are not visable to the naked eye. And the last poster is correct you will need to treat the cage as well.
I wash the whole thing in bleach, dawn and hot water, then I put out to dry in the sun...then spray with Provent a Mite and let dry. You will need to redo this again in 2 weeks to ensure it is gone. You need to put hides in the dishwasher on a hot wash and cook all wood for 1 hr at 225. Mites can be a total nightmare to get rid of.
As far as the humidity....when I see they are going into shed I mist 3 times a day and put a damp towel over their warm hide. I keep rewetting this once a day. You can also create a moist hide from spagnum moss.