.... Using it to effect a miraculous cure, without having invoked the name of the Lord would make Guðmundr's miraculous cure some sort of diabolical black magic, no?

No. There are abundant stories of using a relic of a saint--body parts, items of clothing, brandea (contact relics)--including even of living saints, to effect a miraculous cure, without invocations, and much less without any mention of diabolical black magic. -- Paul