I've used a product called 'Damp-Rid' to battle moisture in basement corners. Most home centers sell it.
A dehumidifier will work, too, but four months of that is gonna use up some electricity, for sure.
I don't know about the rock-salt dessicant. Sounds reasonable
(and cheap). A fan to keep the air moving might help.
Minimize the moisture getting in by making sure your gutters and downspouts are cleaned out and directing any rain away from the slab. Also fill any low spots around the slab and grade away - if you have water pooling around the perimeter of the slab, it can percolate through the concrete and evaporate into the interior.
Good luck! It's always better to keep the water out than it is to deal with the problems it causes when it gets in.

I have a electric dehumidifier with a build in pump so you don't have to keep emptying the water out.

I have been using Dri-z-aire (link below) in boats, basements and cars during winter in PNW with great results- draws lots of moisture especially from cars- cheap and no electricity needed. Best bang for the buck. Be sure to keep it in an extra plastic container to ensure no leaks. If you use tin the salt will eat at it...

http://www.drytheair.com/xcart/store/catalog/product_16133_DriZAir__Unit_with_1_Package_of_13_o z_Crystals.html

You're right...electric dehumidifier removes humidity from the interior of a safe and protects against rust.

No rust tips, but set your heater knobs full on when you store it, otherwise the heater ductwork makes a nice home for mice:eek: