Hmm I think it'd make more sense for the demon king to become the trident. He has three horns with the middle horn being slightly shorter, just like a trident.
Also, Fi is the physical form of an incredibly powerful weapon created by the goddess and she/it clearly has some impressive powers. Powers that could probably only be rivaled by the goddess herself. Which would make sense if she becomes the master sword. If this king were the trident, then his physical form would probably be equally powerful. This would explain why he was able to stand up to the goddess. This would also explain why the Master sword had to be created. Only a sword imbued with the life of the powerful Fi could defeat him. The only question would be: How did this trident demon come into existence?