Did you try removing [ITEMS_HARD][ITEMS_WEAPON] from the WOOD_TEMPLATE?
Did test this by the way: i took both of these tags away together and the only change was that shields disappeared from carpenter workshop. Training weapons were constructable from wood even without [ITEMS_WEAPON] in the wood material believing me to believe that these are purely hardcoded (the weapon raw is accessible, but no reaction ofc). Barrels/bins/beds etc all still built fine from the wood.
I then regenned the world without [WOOD] in the material template, no noticable changes there either, whatever that steers its not related to profiling it as a viable mat for the carpenter.
In both these configurations the wood was still burnable to charcoal too. Hmmm.
Since beds, barrels, bins all are missing from tool raws im guessing these are hardcoded tools that are going around the wood material tags somehow. I'll have to think about this really, i may end up being forced to have my scrap trees actually appear as scrap plants. It appears theres no suitable workaround to this (found yet anyway) since I noticed post-apocalypse also has this issue of 'wooden' items being made from the fake wood.
Thanks again for the pointers Tomi
EDIT: not sure what the issue was last time...i just managed to generate a world with no trees at all, seems the game doesnt care one bit. However it does add a few issues. Namely the wagon logs and any wooden containers you embark with (booze/food barrels) have the ' ' material descriptor. My wagon is made from 3x () apparently, all my barrels are 'Meat Barrel' 'Plant Barrel' etc and everything holds exactly 5 items in a single stack, including the booze barrels so I have lots more barrels than usual, each filled with fewer items. Interestingly the skill to deconstruct said wagon was masonry and not carpentry, it yielded 3x 'logs' (again no material). None of this caused the universe to suddenly implode, but all very hacky and undesirable