This has been suggested many times before, I think, but maybe now's another good time to bring it up... with metals potentially limited, perhaps uses for wood, stone, and bone should be expanded, so low-metal fortresses can put together at least some defenses on the cheap?
Wikipedia has an article that covers some simple ancient weapons that don't require metal.
Wooden spears are simple enough to make. Bone or flint spears, too (well, they're really a bone or flint spearhead on a wooden stick, but you know.) Flint arrows ought exist, too, come to think of it.
Perhaps crude clubs? Wooden maces?
Some people have suggested glass weapons, but those would probably be novelties more than actual weapons... they'd shatter the first time they get parried or blocked, so you couldn't really count on even landing one hit with them.
Stone anvils are at least theoretically usable. They'd impose a penalty, I would expect, but you would at least be able to use one if you had to to keep your fortress from dying off.
Stone axes certainly existed, although you'd usually need wood for the handle. Maybe there could be a 'sharp rock' object that could substitute for an axe when nothing else is available... sharp rocks could be created by craftdwarves and used to make other stone-based weapons. This would be a cumbersome production process, but it's supposed to be.
Slings and darts are also listed as common ancient-world weapons, and frequently used by hunters. Of course, this is a bit unnecessary in DF, since crossbows can be made out of bones... but slings would basically never run out of ammo, I guess, since rocks are everywhere and dwarves could easily grab more.
A pick, that most vital item in any fortress, is quite a bit harder... I can't find anything on prehistoric pickaxes except one mention of using deer horn from Wikipedia, which is tagged with a 'citation needed' tag. Oh well... I guess some things really will require metal.
If your dwarves have no picks at all and are ordered to mine, though... what about this? Much like starving dwarves hunting for vermin, they come up with something. If metal weapons are available, they try and mine with those. If not, they hit the wall with stones or try scratching at it with their fingernails to try and dig very very very sloooowly.
Oh! But, of course, using poor tools would be an unhappy thought. What dwarf would want to use a stone anvil, or try to cut down a tree with a sharp rock, or try to dig through solid stone with their fingernails?