Just returned and we had good weather. It was actually warm in the cities, mid-70's and hotter, and I had no summer clothes. In Zurich, the young folks were sunbathing and swimming in the river, little north of the old town.
We only had two days of clouds and rain, in Murren, which can be expected in the Alps, where we wore our packable down jackets.
A few years back, I was there the end of Sept/beginning of Oct., and in some of the mountain areas it was shoulder season, [between ski season and summer sports] and some of the small shops and restaurants were closed.
I agree, I think you could have a wonderful trip in this beautiful country on your own, without a tour. There is a lot of English spoken, and the train system is friendly and efficient.
In any case, you'll have a memorable trip!