If you dry a wooden cabinet out too much, the wood could either split or get gaps at some of the seams, esp. at the corners. You would be better off getting the gauge, put it inside without opening the case for 2-3 days, and see what readings you get over that time.
Depending on where you live AND whether it is summer or winter, will affect the levels of humidity in that case more than anything you could do. Keep the guns clean, wipe down with a LIGHTLY oiled cloth about four times a year and you shouldn't have any problems.