We hiked it a week ago and one person with us wore running shoes because he forgot his boots by mistake. He had no problems with traction on the snow. There are only two places where you are on snow and they are small areas. As long as you have poles and go slow, you should be o.k. Having said that though, I myself need a boot as opposed to a shoe. I have had some problems with my feet and there are many places where you are walking and navigating over sharp rocks. Even with my boots my feet took a beating, especially on the way down. The other persons in our party had no problems so it's all about how sensitive your feet are.
In regards to the water on the switchbacks, it's not a problem in the morning but in the afternoon, it was flowing pretty good in a few places. However, you're still able to stay out of the water if you're careful.
