Chocking only one direction of a wheel? Maybe making them in pairs, connected together with a piece of small rope (maybe paracord) like the wheel chocks that they use for airplanes to keep them from moving in either direction would be good. The rope becomes a handle when carrying and removing them, and you always have two when needed. Paracord is readily available from Walmart. It's only about 1/4" in diameter, with a tightly woven outer surface like old style clothesline, but the jacket and lining is made of Nylon, so incredibly strong for it's size. I use a cigarette lighter or other small flame to melt the ends when I cut it. I started using it when backpacking years ago. It was light and strong, so good for many uses, and did I say light. When backpacking, every ounce left behind is appreciated as you climb each hill. Now that my backpacking days are far behind, I use it to secure my camera tripod and light stands, sometimes backdrops, when Mother Nature decides to blow a puff of wind at just the wrong time. It's also been used to haul camera and backpack bags up steep cliffs, when it's too steep to carry these bags.
Maybe this isn't necessary, but the idea would look good, and to keep you from "flying" when you don't want to.
Charley