I haven't done any hut-to-hut hikes in Switzerland, but I have hiked to some of the huts on the Via Alpina.
We stay in the Bernese Oberland (either Kandersteg or Lauterbrunnen) when we visit Switzerland.
From Kandersteg, we hike to Griesalp. This is segment 13.
https://www.schweizmobil.ch/en/hikin...ppe-01558.html
The hike to Hohtürli is awesome.
From Lauterbrunnen, we follow segment 12, which takes you Griesalp via the Rotstockhütte and the Sefinenfurgge.
https://www.schweizmobil.ch/en/hikin...ppe-01557.html
We cheated on this one and rode the tram up to Schiltorn hahaha and then just hiked down a bit to the trail that heads to Sefinenfurgge.
We just hopped on the bus in Griesalp and returned to base.
Although not on the Via Alpina, the hike to the Schreckhornhutte is very impressive and should be considered. You access the trail from Grindelwald/Pfingstegg (cheat and take the tram to Pfingstegg). It's about a five hour hike one way.