As a Chicago area flight instructor I've flown the lakeshore route many, many times for discovery flights, photo missions, etc. During the week it probably won't be too busy but on the weekends it is typically pretty hectic with banner towers, sight see-ers, and transitioning traffic. See and avoid is the name of the game. As far as approach causing you issues due to lack of a transponder, don't know but it sounds like others have transitioned without an issue. Have fun!