Nope, that's not universally true. Some companies, such as mine, definitely favor pretty much any random "Bachelors" degree from dubious "universities" in some remote nobody's-ever-heard-of-it location over a solid education from around here.

Every time I read "top university in state X in country Y" when there is only one university in that state in that country, I have to laugh (in reality I want to cry). Happens more often than you think. Yet somehow that seems to go through, but God forbid you should not have a "degree".

Foreign experience counts too, especially in internationally operating companies where realistically most people who write here end up, although of course not all.

Just to add some perspective.

That all said:
OP, transferring skills is always difficult and Switzerland isn't the most, well, experimental place when it comes to that. That said, if you start from scratch in the sense that you do something different here right from the get-go, it could work, whatever it may be. Not sure a few courses will do the trick, but I'm not the SME.

Reading through all of that though, I couldn't agree more with runningdeer than to recommend finishing the interpreting degree. The one in Geneva is outstanding, though it is extremely, extremely hard, but if that's where your passion is, honestly, why bother with much else... Geneva further obviously is the center of many international organizations, so while I'm sure you know how difficult it is to get permanent employment (that's the case anywhere though), there's not many locations that are better to get access to freelance work.