I'll try to go over the basic list of weapon types and what I think kobolds should have for them.
Digging--Shovels. Duh
Woodcutting/Limb Severing--Hatchets.
Stabbing--Spikes/Stakes, Daggers (wrong category?). Daggers should be createable directly from enemy swords and spears and such, and should be the non-crude version of the weapon. As non-kobold-specific weapons should be unuseable by kobolds, this will make daggers very useful, even though you can't make them out of wood.
Combo-Sharp--Daggers. See above. Maybe add some kind of small, swordlike weapon?
Armor-piercing--Clubs. They should have a big head, fairly small contact area, and high velocity multiplier so that even wooden ones are good vs. armor.
Projectile--Atlatls (or spearthrowers, for a non-aztecey feel). Kobolds should also be able to steal bows and make arrows.
Weird*--War-Totems. They'd be a bit harder to make (requiring a special workshop to transform totems into war-totems and perhaps having a chance to produce a syndromey gas mentioned below) but once you do you can have a shaman "chant" or something to summon some charges for the totems, with a chance of producing a strange gas that renders the shaman injured and tired in its wake. The charges would be an ammo type called "charge," with a material called "magical" that has 0 material_value (to prevent trade spam). Totems would be weaker than atlatls, but would have cheaper ammo. Their attacks in melee would use the hammer or mace skill, as opposed to the atlatls's sword- or knifebold skill.
Cheap--Some sort of wooden weapon, like a small stake. Uses the knife skill.
Expensive**--Maybe daggers, since they require you to break down enemy weapons to make, but more interesting is some kind of reverse-engineered crossbow (termed the "crude crossbow" for now). The crude crossbow would be tough to make. The first step would be to break down enemy crossbows, creating "crossbow parts" (tools?) and possibly crossbow plans. Using the crossbow plans (which might be preserved, or might be consumed 1-5% of the time), a bowyer/mechanic in a custom workshop could make a crude crossbow from crossbow parts; using the plans with no chance of destruction, s/he could also make wooden crossbow parts or bolts. Maybe some kind of upgraded war-totem (requiring some kind of sacrifice of wood, food, or blood?), capable of being used to summon "powerful magic" charges, would be neat.
*Like whips.
**No precedent in vanilla, but plenty in mods.