IMO, Gawyn will unwittingly wear all three and meet a tragic end. I think that given the nature of the rings, we can perhaps guess that Gray Men are created in a similar way, and Gawyn will respond similarly. There is nothing said about the Bloodknives' ability to recognize friend from foe, or Lightfriend from Darkfriend. I'm thinking that they might make the wearer somewhat berserk.

Alternatively, another person's blood will come into contact with the rings and they will die as a result.