All the instruments I've seen list off what they need in the description,
which looks like this part on the far left (on larger resolutions it is a small window in the top right of the right most screen). This is the menu that pops up when you select the make instrument option in the Craftswarf's workshop.
You can note in that example it says it is made of 4 parts: Main part is Bone (3rd line) with 3 other parts: a Leather bellow (5th line), Ceramic pipes (12th line), and a Ceramic keyboard/pedalboard (16th line).
That tells you that in this case the instrument is made of 4 parts, 1 from Leather at the Leather works, 1 from Bone at the Craftsdwarf's workshop, and 2 from Ceramic at the (Magma) Kiln. These are then assembled at the Craftsdwarf's workshop (
Single part instruments and instrument pieces say 'make' rather than 'assemble' and well you can see that the single part instruments say what they are made from, (7th line for that one), you'll have to go with the workaround of looking at the assembling of the instrument to see if it is wood, bone, or stone or restricting it so it has not access to wood/bone/stone. (only in Craftsdwarf's workshop though, as ceramic, metal, glass, and leather have their own places they are made).
On the bright side, you can narrow it down rather easily as craftsdwarf's workshop only has wood, bone, fiber (silk/plant fibers/?yarn?), and stone (as far as I know) so if it says "strings" then it wants either plant fiber or silk (or yarn?) (though you'd have to narrow that down as it wants specifically silk or plant fiber, not just any thread. Instrument does note "silk-stringed" or "cloth-stringed" (and "metal-stringed").).
--
As a note, I made the 1st item pictured, and I had -horse bone console- (main part),*horse leather bellows*, earthenware keyboard, and -earthenware pipes- and it used the bonecrafter, so it might base it on whatever the 1st part listed is as to skill needed for assembling it?