Although I'm not really sure about the propriety of granting Galadriel's gifts even to characters that aren't Elves or Hobbits (members of the Fellowship, by the way), if we were to consider a suitable concept, I would choose the latter one too: Galadriel hands to Grimbeorn an old axe belonging to the lost kingdom of Doriath (or to the ancient Nandor of Beleriand), which will serve him to fight the Evil as it had done in the Elder Days (in the hands of valiant Elven warriors). The people of Doriath suffered greatly the constant pressure of Morgoth at their borders; the weapon will just symbolise the same determination to contest the darkness as the one of the Skin-changers during the Third Age of Arda.
Those are really cool suggestions! I personally prefer the latter one. Maybe we could create a poll when we gather more ideas?
According to the current guidelines, polls ought to be established once the concepts proposed are quite finalised; it's the only way to have this feature work properly as it's supposed to do. On the other hand, going more topical to develop further one or multiple suggestions would require the opening of a new thread, exactly appointed to deal with Grimbeorn and a hypothetical gift from the Lady of Light. The very establishment of a poll would thus be much easier as well, as the Lothlórien Brief Suggestions is a too broad of a thread for more on-topic initiatives regarding one sole proposal.
Henceforth, is someone willing to start a new thread?
EDIT: I support Necro's advice