Polished brass shouldn't corrode very fast. I've never seen any corrosion result from letting it sit a couple or three days to dry. Water spots, yes, but no corrosion. That takes being wet for awhile. If you have hard water, a little distilled water as a final rinse will get the minerals that cause spots out.
If you have a vibratory tumbler, pour out the media, place a terrycloth rag in the bottom and put the wet cases in and let it hum a few minutes. That'll shake most of the water drops into the rag. They should then dry fine in air.
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