That would depend on where you live. I live in michigan and called up the state police and explained to him the whole situation about the sword, how it would act as a prop, I would not take it out and it would be on my back and that I would be attending a convention so I would be having it in public. I got a good laugh out of him, but he had NO problem with it at all, but he said the people holding the convention might have a problem with a real sword in public, and if they do, all I would have to do is take it off, put it back in my car and not have to worry about anything.
Another thing you could even do is buy a lock which locks the sword into the sheath making it so that nobody can come and take the sword out. The most familiar method is called peace bonding. You can even do a search: "peace bonding weapons" to read more into it. You basically use a zip tie or a few to make it so that the sword can not be removed. Depending on the conventions weapon rule, you will still need to have it inspected by security so they can determine if it's safe or not.
Hope that helps.