They wouldnt have wasted the time to give him the Uniform and kit of a waffen ss soldier in 6 hours between the attack on the radar station and the town. ALso he may have spent 1-2 hours wandering around france so thats even less time. Steamboat Wilhelm also clearly has a butt chin, so unless the SS gave him some plastic surgery he couldn't have a regular chin like the SS dude who stabs mellish.