I have no idea what the Swiss standard for a CV is. However, you do have the right to get a reference letter from your last employer and I read somewhere that you actually have the right to get a "positive and uncoded" one. Codes: I do not know if you do the same in the UK, but there are certain ways in the German speaking countries to express negative stuff in really positive terms. So it can sound very nice for you but actually means something negative every other HR guy will understand, like "he was always on time" meaning "there is nothing positive about him except that he actually shows up at work on time"... so you should be very careful with the text you get.
Definitely ask for it, if you have no other "proof" of six years work experience. And you already figured out how important any piece of written documentation is...
And keep up the spirit. I do not remember how many applications I wrote but I am sure it was more than 200...

Cheers,

Chris