In my Chaos TL, I have Switzerland (even a Greater Switzerland) despite of a POD in 1200. Then again, since we're talking about Genghis Khan's death, the butterflies don't even reach the HRE until 1240, and Rudolf of Habsburg was already born then. His successor Albrecht was born in 1255, and it may take some time for the butterflies to spread from Silesia to Switzerland... but so or so, the structures would stay the same: Switzerland had free peasants who also had experience in hunting/fighting and liked their freedom. After all, in their famous oath of 1291 they confirmed their "old freedoms". This wouldn't change easily.