Hi,
Welcome to Pakwheels forum.
If not travelling by air from Karachi, then Greenline train service is best for you from Karachi to Islamabad, then you may get rented car for Islamabad to Skardu, and take the route of Naran - Babusar. This route is short and beautiful, you may stay overnight at Naran/Kaghan (your choice).
I am sending you contact number of a person from Gilgit who I trust the most. He has transport company in GB. So you may get any sort of vehicle you want for your desired destination at reasonable rates.
Check your DM.