Those are my home waters, I could walk to both while growing up. Hayward is little more than a slow moving section of river. It is extremely unfertile, and very unproductive. There are a fair number of pimeminnows inhabiting the lake, and a few skinny trout, but not too much to speak of. Once in awhile the beaver ponds by the beach would produce the odd surprise though.
Stave is not a lot better, but it is a little better IMO. BUT there is waaaay more water in Stave to work through to find the fish. And much less shore access. A boat is fairly mandatory to do any serious fishing there, but watch out for submerged stumps and floating driftwood. Many boats have been wrecked/sunk on that lake. If you put in the time, and get a little lucky you can be rewarded, but I guess the same goes for most lakes.
Good luck if you give it a go. At the very least it's a beautiful area to get skunked in