RE: And some things like sneakers/running shoes can take a surprisingly long time to fully dry if they get soaked, even with such extreme measures.
Our "waterpoof" (Gortex lined) boots still get soaked in a rain deluge event. We dry them by first removing the boot insoles then stuffing the boots with balled up dry newspaper (after pouring/shaking the water out). It may take several changes of dry newpaper balls but the paper absorbs the water or at least enough of the water for walking the next day.
While cotton socks are fine for around the town wear, a synthetic (if you can't tolerate merino wool) is a better choice if you are doing serious walking in Scotland. If you look up REI's "Women's Hiking Socks", the REI search filter shows:
Wool / Wool Blend (88)
Nylon / Nylon Blend (4)
Polyester / Polyester Blend (21)
Silk / Silk Blend (1)
Polypropylene / Polypropylene Blend (2)
I like the Cool Max brand of polyester as a fast drying material.
Try/use the socks before your trip. If they don't work (i.e. blisters or fit pressure points) you don't want to find out during your trip.