For any who wish to portray a woodworker in the festival, I've gathered some info which, while not pertinent to Mesopotamian woodworking, might still be helpful.

As pertains to the chore of the wood-workers in the festival, I couldn't find anything in my references on Mesopotamia. However, Ancient Egyptian Materials and Industries by A. Lucas and J. R. Harris discusses Egyptian woodworking. They say that it has been claimed by other authors that woodworking here must have been imported from a land which is more forested, such as Asia Minor, Phoenicia or Assyria. While the authors state that it doesn't necessarily follow that since Egypt had a poor selection of woods to work with, they could not have invented their own technology for carving it, the mere nature of the question implies that Assyrian and Phoenician wood-workers were probably at least as advanced in this area. They describe Egyptian woodworking tools of the Middle Kingdom (2160 BC to 1785 BC) as adzes, axes, chisels, reamers and saws, all, except some of the chisels, having wooden handles; also bow-drills, polishing blocks of sandstone and wooden mallets. At first and for a very long period, the blades were copper, which later gave place to bronze and at a very late date to iron. An adze, shaped something like a short-handled, heavy hoe, was not only used for rough cutting and shaping of the wood, but was also used occasionally for smoothing the wood. A reamer is a tool used to shape or enlarge a hole.