This opens several lines of thought for me.
There could definitely be a distinction in the game between soft and hard metals. One should be able to make crafts, coins, mechanisms, and probably furniture by cold-working tin, brass, copper, silver, gold, platinum, and electrum. A "Metalcrafter's Workshop" could be split from the forge, with the forge reserved for working iron, bronze, and steel, plus copper and silver armor and weapons. You'd still have to smelt the metals first.
Dwarves may be legendary masons, but stone mechanisms are still not very plausible. Wood mechanisms, on the other hand, are. So I think mechanics should be able to make wood or soft-metal mechanisms without a forge.
But not stone. This would increase the importance of wood and/or metal a bit. This in turn could be addressed by adding more raw materials to the starting list, such as logs and metal bars. In fact, those long lists of finished goods available at the start make almost no sense at all. Who brings crafts with them? On treeless maps, though, I'd totally bring 5-10 logs if I could. I'd love to trade for them as well.
Finally, as for traps, I get the sense that you intend for these to be crafted more or less on-site by the trapper. In that case, they should be buildings, not furniture, and the trapper should build them directly, without using a workshop. That produces the somewhat implausible situation of a trapper building a trap out of ingots or a log, so maybe the carpenter's shop should have a "Make Planks" option (equivalent to stone/metal blocks) and the forge and metalworker's shops could "Make wire". Traps should furthermore be buildable out of rope.
Heheh, yet another thought: maybe linking mechanisms should require wire or rope, not mechanisms. One mechanism for a lever, one for whatever it's connected to, and one wire or rope to connect the two.