"…A cotton blend is perfectly fine."
To add a bit, a lot of dri release stuff is made with 85% polyester and 15% cotton. You can get some of these shirts pretty cheaply. Ime, it dries really fast, wicks decently (though apparently differently than the traditional wicking all synthetic stuff) has a nice feel (because your skin is contacting mostly the cotton, which is on the outside of the yarn blend), and is decent at odor reduction.
I'm not sure i would like anything above 35% cotton for anything but hot and dry weather though. Here is the SE, even just doing yard work in the summer in a 50% cotton and 50% polyester t-shirt, not the most comfortable. Whereas a thin dri release shirt doesn't get so overwhelmed with sweat so quickly. A thin, 65% poly and 35% cotton dress shirt is OK, but not ideal when it's very humid and hot.
Btw, Ian, a heads up for yah. I know you like wicking nylon shirts. STP started to carry a Terramar mostly nylon t-shirt for pretty dang reasonable, especially with a coupon. I haven't tried it yet, but plan on getting one in the nearish future.