I have taken several Clay Lake fly-ins over the years to get to Kawnipi.  The Greenwood River that comes off of Clay and leads into the Waiwag is a very zig zaggy shallow creek. It most places it is only about 10 ft wide at best. It can get very low. In fact, one year many moons ago around the 4th of July ... my brother in law and I had to pull our canoe thru this creek almost 3 miles to reach the Waiwag. It was nuts. I would highly recommend going in before the 4th of July to make sure water levels are high enough to paddle through. I see that you are planning on a May trip and that surely would be a great time to paddle the Waiwag.

The water depth of the Waiwag is never a problem. It has good depth. It does however have beaver dams like you have heard.  The last time I was there I remember 4 dams that we had to portage around. They were all quite short and not that difficult to foot.

Another piece of advice is to get an early fly-in time into Clay Lake. It will take you a good 5 1/2 - 6 hours minimum if you double portage to get to Kawa Bay. There are no campsites along the Waiwag ... it is marshy along most of the river. You don't want to get caught with a late start and trying to find a campsite in the dark once you get to Kawa Bay. I usually camp in Kawa the 1st night when I take a Clay Lake fly-in. I have made it to McKenzie Bay on Kawnipi the 1st night but that is a full , hard day to make that the 1st night.

There is a good chance to see moose along the Waiwag. There are several bays that are scattered along it that sometimes are frquented by moose. Lots of mergansers and ducks too.

Bottomline, it is a very enjoyable route to paddle. I highly recommend it.