Probably not a good idea. Picture it for a moment: There you are peacefully perfecting your technique in the light of the dawn. Someone walking through the park catches a glimpse of you, and instead of a peaceful artist they see some guy swinging a really long friggin' blade around in public. The police are called, several officers arrive on the scene, tasers are drawn, and you can imagine the rest. You don't need that kind of hassle.
Here's the problem: Canada actually has very lax laws regarding knives, but very severe laws regarding weapons. Anything can be a weapon if it is or is intended to be used as one, and the use of weapons is really serious legal business. Keep in mind that a sword is designed as a weapon, so you can see where someone might think it is one.
If a cop should see your sword as a weapon, they'll respond quickly and decisively. Before they ask you what you're doing, you'll be told to drop it on the ground and step slowly away from it. If you don't comply immediately, you'll be taken down hard and fast. You'll very likely also be charged. You have a good chance of beating the charge(s) in court, but again... who needs that hassle?