Local school wasn't an option for us at the time as we were both working and needed the extra hours that a private school could offer. When you added up childcare costs and English tuition it was cheaper to do the bilingual route. We also didn't know if I would get a permanent contract at the time, so with that in mind, a return to the UK was a possibility.
We have been to the local school and we are considering it now as my husband is at home, and my son plays with all the kids on the street. My neighbours have come from the UK and their DS is he same age as yours and goes to the local school. He didn't speak any German, and now he is fluent. The Swiss schools provide extra German lessons free of charge on Wednesday afternoons. He is always out playing with the local kids, and I see him doing the trek to school with all of them. As I said there are only 16 kids in his class - so plenty of time for the teacher and assistant to spend settling dc in and making sure they are supported.
We live in what the Swiss would call a town, but actually it's more like a village. Even then there are 6 UK families that we know of here. 30% of the Swiss population are overseas immigrants and not all of them are in private school! A lot are German, but there are also Serbian, Portugese, UK, USA, Indian, Thai etc. Your son definitely won't be the only non Swiss child in school.
It is really hard to get over these fears when you move, I know - but this is a very wealthy country with fewer social problems than the UK, and you don't have schools in special measures etc.
Have you actually visited the area your DH has been looking in? Seen the house etc? Made an appointment with the school to visit? It would be great if you could, as I am sure it would put your mind at ease, otherwise it is easy to create scenarios and concerns that you can't shake off.