If you want to annoy the locals, call them the 'Shetlands' or the 'Orkneys'.And yes, the UK mobile networks should all work fine. Though maybe not much on Three, despite their adverts with the dancing ponies...
It doesn’t matter where you start. Just start.
A FB friend of mine is currently in Shetland and she is posting some wonderful pictures of her holiday there. So it seems she has no problem with her connectivity.
If you want to annoy the locals, call them the 'Shetlands' or the 'Orkneys'.
EE's coverage checker map suggests almost all of Shetland has coverage outdoors.(I used ZE1 0RB, which had been my base in 1989, and zoomed in and out.)
You'll be fine. I had signal even as we tried for the coast opposite Saxa Vord RRH in 2017. And that's about as far north as you can go. There's a "famous" phone box on Unst and a recreation of a long-ship by the side of the road just outside Haroldswick.Hope you don't mind the wind.
The Gardiesfauld Hostel on Unst is nice. Option of camping outside if you want.Unfortunately the brewery on Unst has now closed. But there is a gin distillery if you like that sort of thing.
I live in Lerwick and one of the real pleasures is that if I ride out of town, if I'm very lucky, I can't get a phone signal.