You may be right, but it will need careful preparation.
From several years ago, I remember being told that Hungary basically requires a transponder for every crossing of the borders; however it was not impossible to get an exception with a couple of phone calls.
I do have flown transponderless over Germany, it limits your maximum altitude, though.
As a plan B, couldn't you rent (just for the trip) a little box containing just a transponder, an antenna, and perhaps a small battery? Powered from a lighter plug? Problem would be to get the transponder registered to the plane.