Get a dessicant called Damp-Pruf or Damp-rid ( or any of several other brands. It is sold in the housewares section at places like KMart and walmart. It’s usually sold for keeping closets dry and mildew-free, but it works great in safes, too. I have also seen it used in gun safes to prevent rust.

Safe companies sell it, too, but it’s the same stuff, and cheaper in the mothball aisle.