Perhaps new modular system is in order for weapons? Swords and their smaller forms would be unchanged, since for a full-tang weapon the only non-metal part is some sort of grip, which is negligible enough to gloss over in game mechanics. For most weapons of the DF historical setting and earlier, there were two or more pieces to each weapon. Those pieces, in most instances, could be used for a variety of purposes individually, sometimes on their own. As a few examples:
Polearms:
A spear, pike, halberd, Lucerne hammer, etc. each would need a wooden pole and a metal head. The heads would be forged from a bar, yielding multiples for some varieties, and the poles would be made by a carpenter. A pole could be equipped as a weapon on its own, being basically just a staff, and the heads added on later when a metal industry is up and running. The poles could also be sharpened into basic punjis or spears, used as axles, cut down into smaller hafts, bundled and used as palisades, et cetera.
Example: a Weaponsmith uses a copper bar to forge Copper Hammer Head [2] while a Carpenter takes two logs to make two Oak Poles. The Weaponsmith then combines the parts into two Lucerne Hammers, which work roughly the same way as a staff in combat and could use the same skill (perhaps 'Staff Wielder'). If the player changes their mind before making the hammers, they could also sharpen the poles and/or forge Steel Spearhead [5] out of a bar and attach those to the poles instead, which would then use a Spearman skill since the usage is different from a swung polearm.
Hafted weapons:
Axes, picks, flails and such would use a shorter wooden handle with a separate metal head. The handle itself would function as a club if used without a head. Most of the same heads used in polearms would work for hafted weapons too: an Axe Head could make either a halberd or a battle axe, and a Hammer Head could make either a Lucerne hammer or a war hammer.
Tipped weapons:
ImBocaire mentioned earlier about making leather whips, and then tipping them with metal. The same principle could apply to a number of other concepts, all of which would work similarly. A bar of metal could be forged into a stack of metal points, which could then be attached to whips or to shafts to make arrows and bolts. A bar of metal could also be molded into shot for slings, or forged into darts for a dart gun, which in turn could be dipped in venom or some other syndrome-inducing contaminant. Branching off from this, small rock collection could be ported over from adventure mode to allow for stone 'shot' in the form of pebbles, and chert or obsidian pebbles could be sharpened into arrowheads or spearheads to make weapons slightly better than wood-only versions, before metal is available.
I'm aware that much of this has been done already in various mods such as Wanderer's Friend and Masterwork. I am not aware of a modular, useful-parts system where e.g. a pole can be used as a standalone weapon and then later upgraded to a true polearm. But perhaps this system would be too labor-intensive for many to find it preferable? Personally I'd rather do the extra work of carving poles and hafts, simply because the thought of a two meter all-steel spear bugs me.