Summer in Iceland isn't all that harsh, right? If you're hiking in trail runners already, just cross the streams in those. They'll dry out in ten minutes of hiking. This saves you weight and saves you from having to waste time changing shoes.
It was a bit of a leap of faith for me to learn to do this. In fact, I actually learned by accident. I was hiking back February and broke through ice over a huge puddle on the trail. Both feet got soaked and it had me freaked out a bit since the temps were around freezing. Fifteen minutes later, I was fine.
Boots are a different story. Cross a river in those and you might just ruin your entire trip. They'll take forever to dry out and will more than likely cause blisters. Just one more reason that I'm happy I switched to trail runners.
Trail runners also make great camp shoes. If you like, you can loosen the laces a bit, take off your socks, or do both. I rarely find myself doing either. It's like my relationship with my pack now that I've gone ultralight. I no longer bother to take it off until I'm at camp and actually need its contents. When something is so lightweight and comfortable, you barely notice it.