Check out Snopes...they have a discussion on it there and determined that it cannot be proven (kind of hard to prove a negative). At any rate, nobody could find any laws specifically stating that hands should be registered as lethal weapon. Most likely, it has to do with braggadocio - who wouldn't want to go around telling people they had to register their hands as lethal weapons!
Relative WORKS FOR the State of Washington.
His job (and has been for 30 years) is to REGISTER all pugilists who fight in the state. Most states have this. If you can’t get a license, you can’t fight professionally in the state.
Its not the “hands” per se, but the fighter himself (now herself too). But his office has investigated fighters who have gotten into deep doo doo, and one of the charges is assault with a weapon.
Snopes sometimes gets it wrong.