Hi Anirudh, Yes, it is a very good time to visit Sikkim. The weather will be very pleasant and soothing in this month. You can visit Tsomgo Lake, Nathula pass and do local sightseeing in Gangtok and then travel to the other parts of Sikkim according to your itinerary.
No issues in travelling just check the weather... Usually its not preferable... Weather.comAccuweather.com
I planned my andaman trip this way only...
Happy travel:)