Trouble with plastics is people get hold of brand names like Polycarbonate and apply it to any old stuff, so unless you have experience with your local supply, I wouldn't take it for granted that Polyanything will definitely work.....
FYI. Polycarbonate is not a brand name. Lexan is a brand name of polycarbonate. Polycarbonate is a chemical name as is acrylic, G-10 phenolic, 6/6 moly nylon, acetal etc. Do a search on riot batons and then look at what they are made of. The bargain cheapest ones are made of wood. The next cheapest are acrylic and there aren't too many. The vast majority are made of polycarbonate. If police and military are using polycarbonate for riot batons, why are martial artists still using wood? Just adherance to tradition and perhaps a little lack of education in what modern industrial thermoplastics are capable of.
Do searches on material properties of thermoplastics and compare them. You will find that solid fiberglass, the various reinforced phenolics, polycarbonate and acetal all outperform any wood in terms of fracture toughness and shatter resistance. They compare favorably in terms of impact resistance. In the case of fantastic materials like G-10 fiberglass reinforced phenolic, they vastly outperform wood. G-10 phenolic, by the way, is used industrially in high voltage power transmission lines where strength exceeding steel is needed without electrical conductivity. The stuff is amazing. The problem is that you can't machine it at room temperature - you have to heat it up in an oxygen deprived oven, so unless you happen to have an industrial oven in your back yard, you have to take the raw stuff as it comes from the factory-no knurling, no rounded ends. At room temperature, even carbide tool bits wear out quickly and high speed steel won't even scratch it. You can smash cinder blocks with G-10 phenolic rod and not even scratch the stuff. For fighting stick material, it is has the problem that it is too rigid and tends to hurt your hand. Polycarbonate is much better in that respect, though it scratches and dents about the same as wood but has a much higher fracture toughness so it simply will not break under use by a human.
No, industrial plastics people don't slap "brand names" on any old thing and sell it. Industrial plastics sell rod, sheet and tube plastic stock to manufacturers who depend upon the material properties for their applications.