I can't say 100% what the effects are of getting your bike shoes (or any shoes) wet, and not only wet but wet in a stream or river that probably has a bunch of crap floating around in it (for example, my boundary water shoes which I wear in and out of the water all day on trips always start to smell).

But - mountain bike shoes *are* designed with crap like this in mind:


So it shouldn't be a problem regarding issues like the shoes falling apart from coming into contact with water.

In my one experience with biking shoes that have the "semi-rigid" soles I wasn't pleased, but other people do seem to like them. Along those lines, there are sandals available that seem to be specifically designed to be ok getting wet:
http://www.rei.com/product/765247

Keen Commuter Bike Sandals - Men's