Late September would likely be a bit better for weather, but from this date it is impossible to predict which would be better between the last week of September and first week of October in 2016. I like to travel in September...on average, the best month for weather.
The attached images at Männlichen above Wengen were taken in the last week of September in 2009, on an exceptionally sunny and clear day. Note the jackets. Hard to remember, but I'm guessing that in the sun, the temperature was about 20 or 21 degrees Celsius.
At high altitudes, sunlight can be intense and warming. A breeze makes quite a difference. Absent sun, it would be hard to get up to 20 degrees.
September has a much better chance of being dry than May.
May can be beautiful and warm, or cold and rainy at lower altitudes. The high alpine regions - such as near the Jungfrau - are pretty much shutdown. Not enough snow left for skiing. Enough snow left to block many of the higher hiking trails. Only a few hotels are open, and most cableways are not running. The cograil train to Jungfraujoch runs all year 'round.
October is also between seasons, but not shut down as much as May in the Alps. Still hiking and the earliest part of October is till pretty active.
Please check these links:
This link may be interesting. It suggests that you will have a refreshingly cool travel experience in Switzerland, compared to India, and that you will join the many thousands of people from India that have endured the low temperatures in order to see the alpine scenery. ;-)
Just remember - altitude really matters.
Please watch your spelling, especially when you use the timetable -
The name of the country in English is Switzerland.
In English, Swiss is an adjective, as in Swiss chocolates.
If you speak French or German, the English name is confusing, be because the name of the country in those languages is "die Schweiz" or "la Suisse."