I rang the car rental place up who said that the tyres will be sufficient. He said if there are chains available on the day then they would be included as I had already paid a winter fee. But he was not confident there was any.

He also said the fine for being caught was "only 100 CHF" so would be cheaper than buying them.....

quite surprising for a very large agency! But maybe I am overthinking this. I'm not used to snow driving but I have a lot of experience driving so I am sure it will be fine....