It is one part of a two-part amulet, Ulic has the other half. I'm not sure if he got it from Freedon Nadds tomb or on Yavin 4, but it is a powerful Sith artifact. He used it to kill the SIth worm the Massassi tried to sacrifice him to, then to destroy the spirit of Freedon Nadd. On Koros, he knocked out Aleema Keto with it before he engaged Ulic. During their fight it reacted with Ulic's amulet and the Sith ghosts appeared.
(Kun's amulet is worn at the hand, while Ulic's is worn around th neck.)
PS: I really doubt Traya would destroy the teachings. It's not in her character to prevent her enemies from learning. She might try to use them for manipulation somehow.
The amulet would have its limits though, the idea that it could take down other Dark Lords of the Sith is rather questionable...
Maybe not against the Sith assassins, but I think it would knock out the three Sith lords from Kotor II (Freedon Nadds tomb). They don't seem that much more powerful than the Ketos.
If it wouldn't work on the Assassins, it stands to reason it would not work on Traya and Sion.
The Force persuade things is what, if I understood the comic correctly, what he used against Odan-Urr. He persued him with a few sentences that the Jedi were lost and Odan-Urr was old and dead. Then Odan-Urr died. Sion is also old and dead, not as old as Odan-Urr, but definitly more dead.
If I remember correctly Exar Kun murdered Odan-Urr, he didn't force persuade him into dieing, he did persuade younger Jedi of this idea after Odan-Urr was dead...