If you hold the key upright between your index finger and thumb, and sling it diagonally downwards, you will remove 98% of the water and it will air dry the rest of the way in minutes.
Laundry detergent works best, in my opinion.
The "oxi" or bleach-type additives really make it squeaky-clean, but you must rinse well. They are also corrosive, so I wipe down all my wire stabilizers with light oil, in addition to lubing the clips they are seated into.