Singing and Dancing Sword - Companion, Weapon, or Upgrade?

Question

Can a Singing & Dancing Sword be played on top of another sword, or is it equipped as your primary weapon?

For instance, would the Rapier of Unfairness become A Singing & Dancing Rapier of Unfairness?

This forum discusses the matter, stating that a Singing & Dancing Sword is a companion (that dances to "strike" enemies, needing no hands). I feel that it is a rather uncommon "companion" card, and should be applied and discarded with the weapon it was initially placed with. To keep in line with the previous example, should the player lose their Elf status, their Singing & Dancing Rapier of Unfairness would become a carried item, and the player would lose both bonuses in the process.

To counter the argument, the card does not say Singing & Dancing Weapon, so that the Chainsaw of Bloody Dismemberment would not obviously become a Singing & Dancing Chainsaw of Bloody Dismemberment.

Answer 1

It's a separate piece of equipment that does not use a slot, meaning you still have two hands free for whatever you want to do with them. The card does not depend on you having another weapon in any way.

The concept it represents is a weapon that can just kind of float next to you and attack stuff for you without needing you to swing it ("dancing swords" from D&D and various stories).