A stainless or aluminum shank is not going to eliminate the rust on your hands, because your receiver is made of plain carbon steel, and is rusting. The rust will transfer to the shank, and on to your hands. Wear gloves, or wash up afterward.
Leaving your hitch shank in 100% of the time, regardless of what it's made of, is not a good idea even if it's adjustable and will fit in your garage. Even if the shank is stainless, that receiver is still rusting, and if you leave the hitch in long enough it will become permanently welded into the receiver.