Welcome to My Swiss Alps.
Good to see that you are planning ahead.
Not sure what specific areas you will visit.....?
<<"We are trying to time our trip to have less crowds but most cable cars
still running and many higher elevation hiking trails open.">>
I'll focus on hiking at high altitudes. if you want to hike at lower altitudes, for example in the Emmental, June is good; I prefer late May for that. Cities are good any time of year.
Lots of pictures of the Emmental in this long thread:
The high trails typically open in mid-June, varying from year to year.
Keep in mind that the climate and seasonal weather are quite different at 2000 meters in the high Alps, vs. 400-500 meters in the "Mitteland"
June will give you green valleys at lower elevations, where Spring begins in May or even late April. They are starting to appear as Spring starts up in the high Alps in mid June. Wildflowers in Alpine meadows are good in June.
It also rains a bit in June. Often very nice, but one year a while ago we had 2 weeks of cloudy skies and rain. In 2019, 2 weeks in early-mid-june gave me beautiful weather, with a couple of rainy days that I worked around.
On average, September is best for clear weather and low crowds. I'd pick late September, personally...Some of the green is going away, but it is not yet really brown in the valleys.
Even early September has reduced tourist density compared to the Summer
Early October is good,too. Cableways still run, but things are slowing down, and a few hotels have started to close in th Alps. No issues in the lower areas, more signs of Fall, especially at high altitudes.
The attached image from Wengen was shot on a very clear day in late june....unusual in June.
The images on the Männlichen to Kleine Scheidegg trail ( Th e Grannies' Walk as the locals call it) were shot on approximately September 26th, 2009.
The panorama of Trachselwald, shot on April 14th 2014 was at about 700 meters. A very unusuakl period of two weeks or so of warm suny weather had accelerated Spring a bit. Trees are just blossoming, and the lowest fields are getting green. Alps still have lots of snow, as does the lower elevation ridge of the Schrattenflüh in the mid-ground between the Alps and Sumiswald at about 2000-2100 meter..