I have vague memories of reading about how the sword must actually be a bladed implement because the various spirits of the earth and demons will be unresponsive to a pistol. The purpose of the sword is to cut and to criticize. So long as the magical weapon is not a shotgun, gun seems viable.

If lead is the issue, real silver bullets do exist. Copper bullets also do exist. Depleted uranium rounds are federally illegal but they would also qualify as "a pure metal that is a higher tier than lead and thus not influenced by the spirits" in this context.