Of course the knee jerk answer is a carpenter, but unless that carpenter knows how to make metal tools from scratch, hand hew a log, and fashion his own nails, I’m not sure how really useful they’d be apart from better physical fitness. A carpenter that buys nails at home depot by the box and sends plywood through a table saw likely isn’t going to have the practical skills to survive on a desert island without the modern supply chain.

Traditional woodworking and blacksmithing like that is now mostly a novelty in the developed world. No one really knows how to make their own tools from scratch which is what it’d take to bootstrap carpentry. The best realistic set of skills would probably be knowledge of how to work with fibers to make rope and gather pitch for adhesive. Then you could make a primitive axe that can do most of the hard work in bringing down and hewing trees.