Welcome to the Board. You say

"Does anyone here fly fish at a lake where wading is prohibited? I dont think I can cast far enough to catch anything as the water is really shallow for the first 10 feet."

I know you can cast more than 10 feet to where the water starts to get deeper. Does the bottom drop off sharply from that point? If so this is the one of the best areas to try. Drop offs often produce fish. In the evening as the light starts to fade the shallows can be very productive as large fish move up to cruise the shallows. A cast of 30 to 40 feet is usually enough to get a floating line far enough out to raise a fish or two. Every lake is different of course and some are just plain no good from shore. A trip to your nearest local flyshop will usually get you some good advice on the lake in question.