I don't know. You may want to limit it to a few specific things. There are a few First Nations legends of creatures that can only be hurt by bone weapons. This is a perfect example of a 'natural weapon' since it's not specifically 'manufactured'.
That said, if the bone was worked and crafted is it now 'manufactured'?
What's the difference between a stick and a staff?
Maybe narrow it down to 'hand-crafted' weapons. So, massed produced weapons wouldn't hurt as much: guns, knives, baseball bats etc.. Maybe some cheap swords.
I'm pretty sure most (real) swords are hand-crafted, but I could be wrong.
So, while I like your idea because it has backing in Lore, I think you should make it a bit more specific.
You could just say 'non-metal and/or synthetic weapons'. That covers swords, guns, knives, some bats. I added 'synthetic' to cover newer materials like carbon fibre - (for modern arrows).
But wood, bone, leather(whips), stone weapons would still hurt. And, although that's pretty broad, not many of these weapons are used anymore because they are primitive.
So maybe you could just say 'primitive' weapons. But that might still be ambiguous.