From chitral it's highly not recommended. I had 1800cc and a top of the line engine pulling 130hp and lots of torque, with effecient system..
Don't take your car, the slope from laspur to shandur is really very incline and rough terrain...
If you really want to do this trip, you should hire a Japanese car like Toyota fielder, x corolla, axio..
These cars have outstanding suspension systems and I've seen axio going really fast where i was only going at 10kph..and then i again visited shandur on a gli 1.3 and literally i was flooring it at shandur track, touched 30kph, even crossed jeeps.. Those cars can do this track, providing you comfort in your car.. If its about your car will go or not? I would say i can take it easily but issue is comfort level will be zero, time duration will increase since we won't be able to keep it on 1-2kph for long enough.
So rent a axio, fielder and enjoy your trip.
But don't take your own car.