These suggestions work fine if your only goal is disposal of the bits. However, this is not always the (only) problem when you have a moody dwarf demanding bones on a map with reanimation. The problem is that bones, skin and hair (maybe some other parts too, for certain animals) WILL reanimate, period. You can preempt this by processing the parts before they reanimate (making crafts, tanning, spinning, etc), altho sometimes parts reanimate so quickly that even a quick tanning in an adjacent tanner's workshop is impossible. This is an even bigger problem with strange moods, because they take much longer than regular labors. I have tried many methods for circumventing this problem, and the only thing that really works is Being Very Lucky. That said, I have a couple of superstitions based on experience that I will pass on. These are just my thoughts based on casual observation - I have conducted no in-depth !!science!! on the matter.
Parts from a corpse seem to reanimate in "waves" - that is, you don't see the skin and bones reanimating at the same time. One reanimates, and then awhile later the next one does. What I usually do, then, is butcher a corpse in a "safe room". The entrance is a bridge that you can raise to block egress after the butcher does his job and gets out. On the other side of the room is a short dead end corridor with a turkey (or something) chained up at the end. The skin reanimates, sees that there is no path out of the room, targets the turkey, gets caught in a trap. You open up the room and let the moody dwarf come get the bones. Try to keep all remaining needed materials close to his workshop so that construction can begin as quickly as possible. This gives you the best chance to get the artifact finished before the bones reanimate.
Almost always, when bones reanimate during artifact construction, the dwarf will never resume the job no matter what. However, on one occasion I did have a dwarf complete an artifact after being interrupted. Here is what I *think* happened. A military dwarf was standing right next to the moody one when the bones popped up and he (re)killed them immediately. The moody dwarf was never attacked or involved in combat and was not moved from the workshop square he was standing on while crafting the artifact. He finished the artifact some time later - and sure enough, there was no bone in its description. So my recommendations for maximizing your chances at completing an artifact involving bones on a map with reanimation: butcher, let the first item reanimate, then GO! Have all remaining "ingredients" nearby, and station a beefy military dwarf right next to your moody one for the duration.
Also, Be Very Lucky.