First off all, best regards from Zurich/Zug :) Swiss people are everywhere...
I don't think you're correct that it's not legal to collect data in Switzerland at all (also abroad). As I'm working in the financial industry I know this topic very well and we also had to do a lot research to use GA at all.
It's always the question what and how you collect data. What you can't do - beside you got in upfront the permission of the user - is storing personal identifiable information. That's anyway not allowed by GA - you can't import/save in custom dimension/metrics for example email addresses.
Please check https://support.google.com/adsense/answer/6156630?hl=en as general basic information about this topic.
If you save the IP addresses via IP anonymization, you shouldn't run into problems if you're declaring this in your data-privacy statements. Take this approach: https://support.google.com/analytics/answer/2763052?hl=en
I'm not a lawyer and also not want to give you legal advises, but ours told us that's fine. If you are real paranoid about sending data to the USA - like we have to be - you can exclude your tracking from very sensitive forms.
To go back to your basic question, if you want to find this out via Google Analytics, your key is "cross domain tracking". Check https://support.google.com/analytics/answer/1034342?hl=en for more information in this direction.
The only work-around I have in my mind beside this, is if you start collecting browser-fingerprints yourself and then connect both collections over the finger prints together (that's not save, as your visitors will use more than one device/configuration). I personally would go for the IP anonimization, exclude very sensitive forms and ensure that your data-privacy declaration contains all necessary parts for and offer an opt-out option then you should be on the safe side.
All the best and TGIF :)