Crossed more than a few streams in Alaska and one river in New Zealand in minimalist running shoes that I use for beach shoes.
Lightweight, doubles as camp shoes, dries very fast.
Having a pair of runners is my favorite solution. They will also get you home if you are blister blasted or a critter chews up your leather boots. I am not fond of crossing swiftwater and have baby feet so I don't mind changing shoes.
mike r