In my views, the best time would be early July. I was there after Mid July last year. The pass was open. You can keep your bike in the boat to cross the lake.
And End august/ September will also be good. rains are unpredictable.
October can again receive snowfall at Pass and would be cool in Hunza and so on.
Its better you go before moonsoon. Usually rains come after Mid-July. Rains can block ways in the lower part of KKH e.g. Mansehra to Bisham like year 2010. Its better you come back before mid-July to remain on safe side.
The Khunjrab Pass opening time is 15th June every year.
(daily 10-12 hour drive)
(5 hour drive)
Day-4 Hunza to Passu/Sost
Day-5 Passu/Sost to Pass and back
Day-6 Passu to Hunza/Gilgit
Day-7 Naltar and back to Gilgit (optional)
Day-8 and 9 . Way back
.. You have to keep 10 days in your pocket and Rs. 25K minimum.