Yeah. The way it works is it looks at all skills, removes any skill that has no experience at all or does not have the potential to create an artifact at all, and then picks whichever one is highest experience out of what's left--or sends them to craftdwarfs shop, if there's nothing left.
So while it's perfectly fine to make each person make a single weapon, you can't expect them all to make weapon artifacts if you ever allow them to do ANY OTHER JOB. Most food production is safe, though, since you can't get legendary food. Skills that will influence a mood--moodable skills, if you will--and therefore should be avoided, are Weaponsmithing (obviously), Armorsmithing, Bone Carving, Bowyer, Carpenter, Clothier, Weaver, Engraver (Stone Detailing), Leatherworker, Tanner, Gem Cutter, Gem Setter, Glassmaker, Mason, Miner, Mechanic, Metalcrafter, Metalsmith, Stone Crafter, and Wood Crafter. All other labors are acceptable, and do not directly influence the choice of artifact item made.
HOWEVER. Note that a specific dwarf with a military profession who is currently active in the military at the time of selection cannot be chosen from the "dwarf lottery" that picks the person who actually gets the mood. Furthermore, the dwarf's actual profession, not their highest moodable skill, determines the weight (or how many "tickets" they get) for that dwarf--so a dwarf who actually makes weapons for a living has a 350% increased chance of being chosen for the mood than, say, a farmer with dabbling weaponsmithing, or someone with no useful skills at all. Plan accordingly.