There's no reason for them to become integral parts of the UK, anymore than the UK annexing the Faroes or Iceland. Even then, I don't see why they'd necessarily be a part of Scotland in particular instead of being something like the Isle of Man or Channel Islands in terms of status.
Norn language survival is doubtful. The trade links with Scotland makes its survival difficult, but apparently from what I can tell, it only really started declining because the political class of Orkney/Shetland became Scottish thanks to inheritance. If you could prevent that, it might survive. But even without that, I think by virtue of the islands being Norwegian/Danish the Norn language would survive into the 21st century as at least a severely endangered regional language. In any case, it'll definitely be one of the most English-looking non-English/Scots Germanic languages outside of Frisian (looking at the few attested Norn texts isn't too challenging compared to other Germanic languages).