I'll second the rec for Skye Silks. I've been sewing for 60 years and found their fabrics to be delightful.
In Inverness, I remember seeing the Wee Fabric Shop, but did not have time to stop. And by the way, if you are asking around, I would not use the term "sewing" shop, but rather "fabric" shop. That said, most of the fabric shops are going to be in Edinburgh and Glasgow, so if you are traveling to either of those cities, you should find plenty of fabric shops.
Another option is when you get to each destination, open up Google maps, then key in "fabric shops near me" and see what pops up. You might find some shops in some of the smaller places you are visiting.
OR you could just look online now. Go to Google (search) and search for "fabric shops in Aberdeen" and you will come up with a list from Google like this one: https://www.google.com/search?q=fabric+shops+in+aberdeen
Try that with the other places you've named and see if you find anything. That's how I find most shops I am looking for.