Cotton is bad to stretch with sweat and end up causing blisters and other unfortunate results. Actually acryllic is the best for wicking and foot care--at least that's what they used to preach in Runner's World magazine.
I found 2 pair of khaki hose in a very light weight wool that were sold as uniform socks from Bermuda . . . or somewhere like that. Seems like I got them on ebay, but I've see them around before and since; just can't remember where right now. (I'm old, the meds are kicking in, I've slept and eaten since then, etc.)
Try "knee socks" or some such for seaching.
Jim Killman
Writer, Philosopher, Teacher of English and Math, Soldier of Fortune, Bon Vivant, Heart Transplant Recipient, Knight of St. Andrew (among other knighthoods)
Freedom is not free, but the US Marine Corps will pay most of your share.