You might be better off storing them in a cabinet which has desiccant material rather than trying to keep the whole room dry. Sort of the opposite of a cigar humidor. You'd just refresh or change the desiccant once in a while.
Running a whole room humidifier is a bit expensive due to the power costs.. It is basically an air conditioner. And you'd need to empty the humidifier or have it setup to run into a drain. And you'd hear it running....
In terms of shocking.. a dedicated cabinet would be better. If you walk across a dry room with carpet, you'll build a charge. But if the room is normal and the cabinet is dry, you won't tend to generate a charge just by moving through the room.
Charcoal will suck moisture out of the air and may be a better choice for larger cabinets. But I'd only use a very pure charcoal with mics because you wouldn't want any byproducts to gas off into the enclosed space. Don't use kingsford or anything like that. I'd be very careful about the desiccant choice. Different materials can absorb moisture at different rates. Charcoal can absorb a lot of moisture quickly. I believe silica absorbs moisture much more slowly. So for a bookcase size cabinet, silica might take a long time to bring the humidity down (not certain).
Either way, keeping the mics in a dry area would not result in increased static damage risk when they 'leave the room', as you asked.
Either way, an electronic temp/humidity station will keep you updated on the conditions in the cabinet or room. My house is 27% right now which is pretty damn dry.