The wrench supplied with the Dremel collet chuck is just a thin piece of stamped sheet metal. While it works if used carefully, its thinness means that it's easy to twist it on the chuck and this makes it fiddly to use. What's needed is a thicker wrench that grasps the chuck over a larger area.
All my 3/8" wrenches that are thick enough are parts of sets which I don't want to break up for a dedicated use. In addition, I want the dedicated wrench to be short to fit in the storage box with the other Dremel accessories.
The solution was to make a wrench. A scrap of hex stock was centrally drilled to 3/8" and then a 3/8" slot was milled to intersect that hole. A short chunk of 3/8" rod was attached to form a short handle; more than long enough for the slight torque needed to seat/release the collet nut.
The resulting chunky wrench can grasp the entire length of the collet nut so twisting is no longer a problem.