You can purchase moisture removers for safes. I use this one (available for under $10 shipped on eBay):
http://cgi.ebay.com/Gun-Rifle-Ammuni...item439815cee2
I believe they are made for gun safes where the metal on the guns can rust easily. However, I have not heard there is any issue using them in safes where you store documents or cards.
The nice thing about the one I pictured above is that the crystals that remove the moisture can be re-charged, so it is essentially good for life.