Mode S is mandatory in Germany where a transponder is mandatory. Unfortunately, the area around Friedrichshafen is classified as one of the very few TMZs (transponder mandatory zones) in Germany. The reason is that Friedrichshafen has quite a lot of big birds doing IFR but when leaving / before entering the control zone, you're in airspace E.
It is possible to request an exemption with the German AIS (+49 69 78072500). Usually not problem but in this case, I'm a bit pessimistic. You might consider one of the other airfields with shuttle bus service (e.g. Markdorf or Konstanz).
PS: No IFR arrivals at Friedrichshafen below 1.6t during the show.
PPS: Don't tell them you don't have a Mode S capable transponder, rather say that it's out of service and your backup is Mode C only.
PPPS: On every 2nd flight I hear ATC saying something like "I only see a Mode C signal from you, just for your information, continue".