Would this story idea intrigue you? Would you want to read the book based on the synopsis?

The idea is sound and if your writing is as good as your imagination it should be a good read. However you do need to have another reason for sending out a prince to look for something which no one believes in into a dangerous environment from which no one has returned. There needs to be some sort of proof of the red swords existence such as an old parchment or maybe an old man who has handled the sword. That would then give the expedition the credibility it should have. Good luck with your story.