Don't believe that gallery those pictures must have been taken on the 3 days a year that its isn't blowing a gale and slashing it down with rain.
There is only one tree on the island for a very good reason.
I would stop in Orkney as well. There are a raft of things to see and do there compared to shetland. The tower used to do fixed period landing and parking cards for all the Orkney airfields for an extremely reasonable rate. There is a private field in Orkney just to the south of Kirkwall. The owner is a star and very friendly and folk have camped there before.
I would phone first to find out the price of AVGAS in Wick before you start planning to uplift there you may get a bit of a shock if you don't.
My route would be up the east to St abb's, wx dependent east coast or through the hills via the A9 to INV uplift fuel there. Then up past Dornoch (worth a land there and a walk on the beach) Past Wick to Orkney and up to Fair Isles then personally I would go back to Orkney.
On the way back fill up in Kirkwall then down the west coast maybe western isles and Barra beach landing as your in C172 then over to Oban to get the plane washed and refueled by the famous Paul. Then down past Cambelltown, PIK and where ever you like after that personally I would head to the west of wales cause I like snowdonia.