Agreed with mohsin, the shortest path from Lahore (or Islamabad for that matter) is through Naran. its a much better quality route, about 150km shorter and much more picturesque but unfortunately due to collapse of bridge at batakundi about a week ago, it is closed. I made that trip about two weeks ago, at that time the bridge was there. it was easily doable in 6-8 hrs that means one can easily go from naran to hunza in a day with stops at lulusar lake, babusar top and maybe one or two more stops.
Not sure if they are going to repair that bridge anytime soon. The only other option is through besham, dasu, chilas but that is about 150 km longer and not in very good shape. Maybe you should try calling the PTDC Naran, they might have information about the latest on batakundi bridge otherwise to phir old KKH route hi hai