I think the shirts do work, but I worry about them feeling itchy (DH has one that he wears with an underlayer - without that it's itchy). I know lots of people don't have issues with that, though. DD doesn't have any issue with the merino shirts.
I will 2nd or 3rd the baselayers for a trip like this. It also can cut down on washing. We found that the "technical" fabrics also hand wash well and dry very quickly.
We did carry-on this summer in the Med - it was easier than our trip to Norway, but it's always tight for that long of a trip. For Norway, I brought regular running shoes and waterproof ones (needed those a lot). Unlike other parts of Europe, wearing North Face/REI/Lululemon type clothes is really common. You don't need to dress up to fit in with the locals. And remember to bring layers, layers, layers.
Shoes are the toughest part of the carry-on packing for me. I generally bring flip flops and a pair of thin (easy to pack) ballet flats along with my tennis shoes. Oh, and I learned from a friend to bring older running shoes that are still good, but don't have much life left in them. That way I don't have to bring them back home (making more room in my suitcase).
I was in Norway for a week in early September a few years ago. It was often cold and rainy, but there were also some sunny days. Just be prepared for it all.
I hope this helps.