You should be ok, If you can, just open the door a few times a day to let to room come down in humidity a bit.
A REAL cheap but effective unit are the Eva-Dry Silica Dehumidifiers:
http://www.eva-dry.com/
Its a box of the silica balls they put in shoes and stuff to absorb moisture from a product while it sits on a shelf.
This box of them will absorb the moisture from the air, then one the balls change colour you can plug the unit into the wall and it drys out the balls back to the "dry" colour to be reused agian and agian and agian....
Availiable at Walmart for $20-$30.