Others can hold it and sometimes wield it, maybe, but it all comes down to the fact only the one with the reincarnated Spirit of the Hero who has proven their strength can pull the Master Sword from its pedestal.
To be fair, Lost Woods doesn't mean just any one location; there's multiple Lost Woods that appear in locations all throughout the series. In my humble opinion, Lost Woods are a term used for woods cured by magic/dark magic. For example, The Lost Woods is found in between Kakariko and Death...