I would scrap the silica gel idea. To dry your sweaty clothes they need air.
Hanging is best. But where? You don't want to make enemies hanging your stink in the community closet, next to someones Brioni suit. The coat rack standing in your office would be a conversation piece, but in poor taste.
Since you don't really need to worry about theft, perhaps you could find a supply / maintenance / janitorial type closet.