Here's what you can do:
1) Place the whole bunch of grapes in a big pail of water.
2) Put on a pair of gloves and work some toothpaste into a smooth lather.
3) Wash the grapes with those toothpaste-lathered gloves, while removing the grapes from the stems.
4) Once done, rinse the destemmed grapes 2-3 times in running water to remove the toothpaste (or a few times more if the grapes are minty!)
5) Pat the grapes dry and eat/use! (I froze mine for a refreshing treat!)