Links between The Hobbit and The Lord of The Rings. A Morgul-blade is created for use on one person only. And how could the Nazgul possibly get a hold of the blade again if it's in Rivendell? No, the Morgul-blade that stabs Frodo was created much later.
"Grave and thoughtful was her glance, as she looked on the king with cool pity in her eyes. Very fair was her face, and her long hair was like a river of gold. Slender and tall she was in her white robe girt with silver; but strong she seemed and stern as steel, a daughter of kings."