Hi, we moved to Switzerland from the UK with 2 non-German speaking children 7 years ago, and put the eldest straight into the local school. Despite a few teething troubles, it all worked out in the end. We were able to start from age 5, and that made things easier, but I know people who did the same thing with older children and the children coped. The Swiss state schools are, in my opinion, far better that those in the UK, and as others have said, there is plenty of support for non-German speaking children.
My husband is also working in Zurich, so we initially looked at moving there. We were, however, nervous about school choice. Your address determines your school, and finding accommodation is not always so easy. Co-ordinating accommodation with the school is yet another complication. We also heard some horror stories about people who had been assured they would be assigned to one school suddenly being told that was incorrect, or a sudden influx of children into one school meant the allocations must be changed throughout the area. That isn't meant to happen, and it may have been prospective landlords/relocation agents trying to push their properties, so I may have been misled on this.
We ultimately went outside of Zurich (canton Zug). In a village, you are absolutely certain which school you will be allocated wherever you live in the village, and commuting to Zurich is nothing like commuting in SE England. Also, where we are has a high proportion of English speaking residents, which meant the school is used to English speaking children e.g. native speaking English children have separate English classes as they obviously know the language better than the Swiss children. Much as one wants the children to integrate and speak German, it can be a comfort for them to have some children in the class with whom they can communicate at the beginning e.g. my younger daughter was recently asked to assist a newly arrived English speaker in class by clarifying the teacher's instructions, until the boy could manage on his own.
There are a lot of language courses you can use outside of school to help your child learn German, but I found the best thing was simply to invite Swiss children home. I found the Swiss children were more comfortable in our home when they came in pairs, probably because we were speaking English/bad German.
If you are interested in living outside of Zurich, message me privately and I will give you details of where we are, more about the school and our experience with it. Let me know if you have any specific questions.
Best of luck with the move.