Ken,
You can book golfing holiday packages from the UK to Switzerland so a special licence with written test etc is unlikely HOWEVER you will probably need both a valid handicap certificate (possibly from a club rather than an on-line one) and insurance.
I don't think that "Pay to Play" is as readily available on continental Europe as it is in the UK or US - as you say private
clubs mainly - but I know that in French
clubs at least if you ring the secretary a day or so before and very politely do the "I'm here on business / holiday .... if you are not too busy ... perhaps I could play ... perhaps .. with a member" bit you'll 99.99% get on - doubt if Switzerland is that different.
Good luck.