Good morning and Welcome to the Forum.
I appreciate your concern about your boys, but it is very difficult for anyone to say exactly what will happen in your case.
I think one problem with attending International Schools initially and then changing over, is that the syllabus at an International School may be in part different from the Swiss one. When our children changed countries, it was sometimes the content of the lessons themselves (knowledge of local Geography - or lack of it, History from the point of view of the country they were living in etc.) which caused 'problems'. As you are intending to stay, remember that the children will learn German more rapidly in an environment where German is the everyday language.
If you do a bit of searching (understatement of the year!), you will find quite a few Threads in Family Matters/Health on the subject of children coming to Switzerland without speaking much German.
From those Threads and the other answers you will undoubtedly receive here, you should be able to find a couple of pointers.
Good luck with the move.