Hey Capt,
I managed a Westwind for 5 years on the gulf coast (JKA and 4R4). We never had much problem with moisture inside of the jet. We flew 3 to 4 times a week which should be enought to dry anything out. If the jet was to sit for long periods, maybe 2 months at a guess, you may start to get a musty smell in the cabin. We just had the jet in a community hangar with the door close all of the time, but never had any problems.
I worried more about the moisture on the airframe than inside. CORROSION! Never any problems with that either. We washed the jet at least every other week and I kept stuff lubed up. Nothing like grease to displace water.
If I had the option down there I would want a climate controlled hanger. Good for the jet and the people working on it. If you put a dehumidifier inside the jet, how is it powered? If you use an extension cord, so you leave the door open? If so, it will never get dry and I personally would not want to shut the door on the cord. Not very good for the seals and if a Westwind is your ride, then the cabin door usually dosen't need any help developing new leaks!
Hope this helps
Take care