Thank you all for comments in this excellent thread! I gathered a lot of insigth why things happened why they did, and how to solve the issue in the future.

Fee (80 chf) was clearly quoted by service rep, and I accepted it. No problems/wrong doing with this particular fee, since I was just looking to get the booking done. The 80 CHF is not a deal breaker for me, regarding this award, I just generally think that it is quite a lot of money. However, since I plan to do this in the future as well, I though it would be nice to gather some insight how to reduce these costs in the future.

I have already 3 excellent solutions that I´m planning to try in the future:
1) Shop around for different service rep
2) Book it on the phone, Pay it online.
3) Got my self EUR nominated swiss CC (Visa).