The composite skills idea might make some people uncomfortable, but it would reduce total skills, while still maintaining choice, precision and specialization options.
If we had three (possible) skill components (material - tool/process - product), and reduced the skills in each category to eg. a mere 10; then we would still have 1000 different possible skill combinations. This would satisfy the desire for simplicity (a limited number of skills), but still allows flexibility and specialization.
For example, we might order a dwarf to use only steel, but leave the other two categories open. He would make all kinds of steel products and be quite good in steelworking. However, we could let him specialize further, and also limit him to only armour. He'll have less to do, but his skill gain will concentrate on steelmaking and armour exclusively. Finally, a player who wants an assembly line of armour could limit him to use only a burin, and thus create a hyper-specialized steel armour engraver that delivers astonishing quality.
This could be adjusted on the fly as the growth and needs of the fortress dictate. As long as you only change one or two categories, it's almost certain that a dwarf's new job will have some skills in common with his old job, so dwarves that change jobs are not as skilled as newly-born peasants in their new jobs. It also guarantees that immigrant skills will be somewhat useful: you might not need a woodcrafter, but he still won't be a dolt at either stonecrafting or carpentry.
Applied to the OP's suggestion, for example furnace operating would be part of the pottery job (clay + potter's wheel + furnace operating), charcoal burning job (wood + furnace operating), lye making job (ash + container + furnace operating), etc. Instead of half a dozen different metalworking skills, we'd have the weaponsmithing job (metal + anvil + hammer + forging + furnace operating + weapons), blacksmithing job (metal + anvil + hammer + forging + furnace operating + furniture), etc. This way you could train a weaponsmith a bit by letting him make wooden weapons, he'll train half the necessary skills that way, but he won't learn as fast as by making weapons directly.
One could choose to have a skill for each metal, for groups of metals, or for metals as a group. That's a design choice and will surely be moddable.