im not sure if it would help much to build a box.
Also, you should get a tent instead of a box in case it gets wet for any reason. A box would just absorb the moisture and eventually warp and mold (depending on the type of wood)
With a tent you can wash it, theyre fairly water resistant, and youll use it forever because it wont fall apart and its made to be taken down and moved.
OH! i have a little dehumidifier i got from amazon a while back. It only does a liter and a half a day but itll help when you shrink your space down to a box/tent.