As it is near the end of August, and therefore the summer, I thought that the muskies would be hanging out in the deeper water, where it is cooler. That may be the case for the bigger fish in the lake, but I now think that the smaller, and medium, muskies are still in the shallow weeds looking for food.
If we're going to fish a weedy lake, the early spring will be your best bet. In the spring there will be a whole lot fewer weeds. Fishing a weedline is good, but when nearly the whole lake is full of weeds it is difficult to catch anything other than the weeds. Fish there before they grow.
Traditional spinners, as opposed to in-line spinners, are a good bet for fishing the weeds because they are weed resistant. But you still want to avoid the dense weeds. Otherwise, all musky lures will work, when they are cast along a weed edge. Lake Wingra has few defined weed edges and is difficult to fish, for that reason.
You can cast into the thick weeds with "weedless" lures but even if you don't get tangled, any fish you hook will.
Look for the weed edges in the small weedy lakes, and cast along them. The muskies will be lying in wait, for the baitfish to swim past. While you are there, don't forget to cast at any points, humps, any man made structure you find.
My day on Lake Wingra was slow and dealing with the weeds was tiring. But a 38" muskie hit a lure twice, and I caught a nice largemouth bass. (If you catch a big fish take lots of pictures; this picture does not do the fish justice. Read my thoughts on better picture taking here.)
These weedy lakes are not the places to catch monstrous fish, so you may as well enjoy trying to catch many smaller ones.
(On a side note: sunburn hurts.)