Swiss Folklore Shows - Any Recommendations?

Stadtkeller is fairly unique if you really want a full-on show in a restaurant, but this should run again next summer on Harder Kulm in Interlaken: https://www.restaurantharderkulm.ch/en/events/events-detail/article/swiss-folklore-evening-harder-kulm-top-of-interlaken.html
Zurich is not really the place for alpine folklore, but there is a little pub (the Älpli bar) that has traditional music - but it is definitely more of a bar than a restaurant https://www.zuerich.com/en/visit/nightlife/aelpli-bar
You don't say exactly when you're going, but on the 2nd weekend of August, there is always a big folklore festival in Zermatt. And August 1st (Swiss National Day) usually means plenty of folklore options in any of the mountain towns. These are not necessarily "shows" in a restaurant, but often there's a barbecue or similar with musical entertainment, flag tossing, etc.
Otherwise, I'd consult the tourist offices and see if they know about any specific events during your stay. There are a lot of smaller folk or music festivals that pop up during the summer.

the Swiss traditional yet very modern family group Oesch's die Dritten https://www.oeschs-die-dritten.ch/en/concerts-2/ have concerts and other performances all around Switzerland and neighbouring countries year round. If you are lucky to catch them, maybe even at a festival, you will be rewarded. Named because there have been 3 generations in the family band. At the moment the daughter, Melanie, is the lead, and she yodels and sings beautifully and enthusiastically in a local way - they are from the area of Kanton Bern in a tiny village deep in the countryside above Lake Thun. Her father plays a traditional Swiss accordion, a Schwyzerörgeli. Mother sings and plays tambourine. Her brothers make up the rest of the band (with friend Urs). For a taster search on Youtube. They have many videos. A good example in various settings (but a few years old) is https://www.youtube.com/watch?v=4wcyGVvPZxk