This all sounds like someone trying to invent problems which don't exist.
If anything, the petition seems to be trying to get the government to include things which are not and never have been weapons into legislation which is nothing to do with traditional dance.
Anyway - traditional activities are by any definition some form of historical reanactment. The key point in existing legislation as aplied to REAL swords and weapons is tha it must be an official group with public liability insurance. That pretty much covers Morris and sword teams.
Quack!
Geoff the Duck.