I do the same thing when we are traveling and are in a location where you are not supposed to put paper in the toilet (mostly on scuba diving boats with marine toilets). I do it sitting on the toilet after emptying and just let the water go into the toilet. Then dry it off with a little toilet paper. I don't worry about the resto of the pouch (it's just going to fill up again).

Otherwise I use folded up toilet paper to wick out the neck of the pouch.

@fbt217 so you have an ileostomy or a colostomy? How often do you need to empty?