Ok, I know that I'm way too late to give any useful help on this one, but I'm going to add my perspective for the sake of anyone else who searches through old threads and has a similar problem.
I live in a cold climate (interior Alaska) and humidity below 20% is quite possible, both in winter and summer, and for extended periods. I've been playing hammered dulcimer here for about 9 years and (pause while I knock wood
) my dulcimers haven't developed any cracks and have been kept reasonably in tune. My house -- an old log house -- used to stay below 20% humidity in the coldest few months of winter until we did some serious energy efficiency work, which sealed up enough leakage that we can keep reasonable indoor humidity most of the time now.
For a wooden instrument, the big difference between adjusting to a temperature change versus a humidity change is speed. With temperature, the instrument reaches thermal equilibrium with its new surroundings pretty quickly and then you can tune and it will stay. (I regularly transport my dulcimer when it's well below zero out -- it was -25 F last night when I went out for my usual Wednesday night coffeehouse gig.) With humidity, the change occurs much more slowly and over a much longer time. I'll suppress my urge to get too technical here, but the rate of change in both instances depends on the difference between the state of the wood (whether temp or moisture content) and the state of the surroundings. That means that the instrument will change most rapidly at first, and then more slowly as it gets closer to equilibrium with its surroundings. It just takes a lot longer for moisture in the wood to migrate to the surface and evaporate than it takes for heat to penetrate the thickness of the wood, so humidity adjustments take a very long time to reach equilibrium.
YOU DON'T WANT TO LET YOUR DULCIMER ACHIEVE MOISTURE EQUILIBRIUM WITH SURROUNDINGS THAT ARE BELOW 20% HUMIDITY. So, leave the dulcimer out for half an hour to an hour to allow it to reach thermal equilibrium and to let it shed a little of its most rapidly lost excess moisture. Then tune it, and PUT IT BACK IN ITS CLOSED CASE until you're ready to get it out to perform. The closed case will dramatically slow down its moisture loss. The instrument will just keep going flat if you leave it out, and that tendency will take many days to level out. If it's a short gig you'll be fine. If it's a long gig, you may need to take a break in the middle and retune.