A good question, one of the many filmation left unanswered on eternian magic.
It seems logical that anyone can use the sword, if they know how, and unlikely that it was ever linked to Adams DNA or voice recognition.
Filmation was never clear about how magic worked and it hurt the story value sometimes.
..(it works in Harry Potter, because all cute boys are magical, or something)
..although in that one episode cringer touches the sword to Adams skin and speaks the power of greyskull line and it worked.
If they are ever going to do this thing as a solid storytelling movie then they need to difine magic better than alot of shows or movies ever have.
I think Masters has alot to do with blood magic and rock magic, and ethics.
..(at least it does in my work)