Cellist dropping in here. Humidity control is a good idea, but overall it's more important to maintain a level than to try to keep the case at some level different from the room or local environment. It's the rapid changes in moisture level that stress the wood (within limits, of course: 0% RH is a bad idea, etc. ) .
Your instrument should definitely be wiped down after every use. Sweat & body oils are not friendly to wood (or the varnishes & stuff on the wood). You should see how many cellos require refinishing on the top of the body where the left hand rests, after 60 or 80 years of use (seriously). Wipe down the strings for the same reason, tho' I'll grant that a good set of guitar strings costs as much as one mixed drink, while a good set of cello strings is slightly more.