So, do you have to wear boots or trailrunners? Did he specify that? If you can wear trail runners, I would take one thick pair of wool socks, and two pair of nylon dress socks. I am a recent convert to dress socks. They breath amazingly well, don't blister, don't overheat, and dry real fast. Take the wool socks in case of climatic weather changes, just in case.

As for the leader, I think you can ask him why his rule, and I am sure he would allow a sock with 84.5% wool, or any mainstream hiking sock with no cotton.