A common question at a sword fighting school is whether it is legal to carry a sword through the streets of Vancouver. This article from the Iaido Journal goes into some length about the legalities for martial arts students carrying swords to and from class. It's a worthwhile read to better understand your rights.
The article gives a more specific view of what our own research has already told us: In Canadian law weapons are generally defined by intent rather than by make (except in a few specific cases). If you're carrying a baseball bat and you're on your way to play baseball then you have a tool for playing the game. If you're on your way to the house of an ex-lover, the police might see things differently. The same is true for carrying a sword, if you're carrying it for self-defence it may not be seen as fitting, if it's blunt and you're bringing it to your swordplay class there shouldn't be a problem.
The most important thing for a swordplay student is to cooperate with the police, be friendly, show them that the sword is not sharp, and be understanding that an inquiring police officer is just doing their job.
I've found that most police officers are genuinely interested in what you're up to with a sword and my experiences have all been positive. Some have even lead to members of the VPD coming and trying out classes.
For added ease, carry a Duello flyer or business card with you so you can further back up your activities. Also putting a bag over the hilt of your sword (if you're carrying it in your hand or strapped to a backpack) will make it virtually unidentifiable to general members of the public.
If you've had any interesting police encounters while carrying swords around the city, share your story in the comments.