It rather depends what your objectives are. If hiking high up is a priority, then late mid-summer is best, when the snowline has retreated and the days are long. The weather is not all that predictable, but looking at averages August is a month too avoid (can be very hot too).
Switzerland is actually quite diverse. The best hiking area is probably Graubunden in the east. Here you will find a wide expanse of unspoilt mountains, isolated mountain villages, high altitude lakes, etc. But then again, Ticino in the south is very nice too (and warmer), especially around the high lakes such as Ritom and Naret, and the Mt Cristallina region. High up, more or less everywhere, you will find marmots and ibex, and the marmots in particular are most photogenic in the late summer.
You do tend to find constant reminders that these mountains, whilst spectacular, are very much an exploited resource. Most lakes are dammed for hydroelectric plants, and the Swiss genius for civil engineering is everywhere.
Finally, for hiking, be sure to check out the Post Bus network. It is almost certainly the most comprehensive public transport network in the world. Generally speaking, if people live someplace, it is a Post Bus destination.
Hope that helps - check out my web site for some photos (see Ticino & Swiss Alps galleries in particular)