I don't know that you will be getting a great deal of sightseeing in - a quick plot with NavBox and a 172 reckons 4:20 for Biggn-Sumburgh at FL050 for nil wind with a few beacons thrown in, and some quite long over water legs. A couple of stops and avoiding long over water is going to put you at around 5 hours.
Never been to the Shetlands, but can recommend Orkney!