Food dehydrator works, but keep in mind there are likely to be traces of lead compounds on the cases that can contaminate the dehydrator for future food purposes.
In using wet cleaning methods, I rinse the brass, drain it and shake it a bit to get more water out, then dump the brass onto an old towel and bounce it lightly and move it around in that until the water in the flash holes and primer pockets has loosened and been picked up by the towel. Then I set it out, mouth down, on a retired cookie sheet, and just leave it alone to dry for a couple of days.