I did this tour in a mid-June, so different than late August or early September. I will say it was the only tour out of 12 RS tours (and 13 Road Scholar tours) that I wished I had had waterproof rain pants and waterproof shoes. In spite of excellent waterproof jackets with hoods we got absolutely soaked on the Oban/Mull/Iona day. The tour hotel had wonderful heated towel rails so my clothes dried fairly quickly as did my shoes. I pulled out the insoles and unlaced them most of the way placing them on the floor under the towel rail.
@JenBlum - good packing list. I'd cut one of the pairs of pants though you didn't ask, lol. I always wear jeans on the airplane so I take them whether people recommend it or not. Mine are Gloria Vanderbilt Amandas and they dry overnight anyway. Yes to the beanie and lightweight gloves/glove liners. When I went to Orkney and Shetland last summer I added in a ball cap although I am not a ball cap wearer. It worked really well under the hood of my rain jacket to keep the hood in place and water out of my eyes. I'll add that a few times I wound up with the beanie on over the ball cap under the hood, lolol.
For Orkney/Shetland I did take rain pants. I packed the rain pants, rain jacket, hat, gloves, beanie in a large size Eagle Creek compression cube. This fit perfectly in my Sea to Summit lightweight day pack and I always had my gear with me.
For both of you, Scotland is pretty casual. No real need for any "nicer" tops unless you are planning a special meal out in Edinburgh or Glasgow or are adding time on to the tour. I find on many tour days you go directly from day activities to dinner with not much time in between.
No umbrellas needed either....the wind in Scotland will just immediately turn them inside out, lol!