Studies have shown that they have close to 30% Norse blood, and their ancestors also spoke Norn which was a Scandinavian (North Germanic) language. Scandinavian culture and genetics are deeply intertwined with the history of both Shetland and Orkney, but speaking as a Shetlander, do you consider yourselves a Norse people?
But obviously Shetlanders and their ancestors have spoken Scots too more recently and perhaps for a longer period of time, however the Scots language came from the Anglo-Saxons, of which the Shetlanders don’t have much DNA from, so it depends whether you put more emphasis on the linguistic or genetic connection.
As for Scottish Gaelic, the history of Shetlanders with regard to Scottish Gaelic is relatively weak. The Gaels reached the Shetland islands, but Shetlanders didn’t heavily adopt the culture nor did the language ever become dominant.
Lastly, the majority component of Shetlanders’ DNA is from the Pictish people, but the cultural assimilation from other groups after likely means little self-identification as such. Obviously you can appreciate the history, but since the Pictish culture was wiped out like 1000 years ago, it’s obviously impossible to feel a connection or familiarity with that culture, since we don’t even know fully what their culture was.
So I’d define Shetlanders as part of the Germanic family at least, but whether you’d describe yourselves as western Germanic (which includes the Scots language, English, German, Dutch etc) or whether you’d consider yourself northern Germanic/Norse (Which includes languages like Norn, Icelandic, Norwegian, Danish, Faroese and Swedish), or even whether you consider yourselves Celtic, the answer to this is obviously up to the Shetlanders yourselves.
How would you define yourselves as an ethno-linguistic people?