I just returned from a Bike Tour from Karachi to Swat, to Gilgit to Khunjerab and back to Karachi about a week and a half back.
And I can assure you its very very safe.
Chilas to Gilgit is not a bad ride, plus you will constantly pass FC Officers in black shalwar kameez patroling the KK on foot. Plus plenty of army jawan at most bridges as well police mobiles passing you from time to time.
I got a full tank of fuel in Chilas which was more than enough till Gilgit. The only stops you will have is for photography and drinking water.
Its a safe track these these days with all the security in that region.
Sulaiman