I keep a small oily rag in a plastic bowl with a snap on lid on a shelf in the cabinet. I give the outside metal a quick rubdown EVERY time I put them away.
The Hoppes#9 has a rust preventer in it. For long term storage I leave the bore well oiled.
The FMJ could be corrosive, esp. if it's old, or made overseas.
Showers probably not the problem, but you might see what you could do to reduce the moisture in the room.
