Jay (Eire)
12463
I would be concerned about the Swiss law while carrying multiple watches.
As I understand it, and you should read the laws yourself, if for personal use all is OK. But personal use sounds a little bit of a stretch for anyone outside of here if you’re carrying multiple watches. There is a document called a Carnet which may be relevant in this case for you. I’d think you want the US form and the Swiss form.
FWIW, I was stopped last fall at Geneva airport and when I told them my reason for travel/destination (which was watch related) they did of course take me aside and search my bags. I was not wearing or traveling with any watch (I told them that, but they obviously didn’t believe me).