Not at all, Canadian regulations define any air gun with a bullet energy greater than 6J(oules) to be a firearm.
For comparison a .22 Short bullet, which is the least powerful mass-produced caliber and considered underpowered for anything larger than a rat, starts at 60J. The .30-06, the most popular hunting round and the smallest thing you'd want to use on a bear, is around 4000J and more powerful rounds well suitable to stopping bears can easily top 6000J. So the most powerful unrestricted air-gun you can buy without a license is literally 500 - 1000X less powerful than what's needed.
Just get a can of bear spray. You can get it at any outdoor store in Canada, it's convenient to carry on a belt and is more than enough for a Coyote or a Cougar. Just make sure you try it at least once (there's more than enough in them for a quick test spray), to remember how far the droplets go(and how wind affects it! Spraying upwind is a great way to use it on yourself!)
Technically crossbows don't require a license, but you won't hit anything without a lot of practice, they are way less convenient to carry loaded than guns and if you kill e.g. a cougar with a crossbow because you say you felt threatened, good luck proving you're not a poacher if someone noticed, so just stick to the bear spray.
I just remembered that technically, flintlocks, including modern replicas, are legally antique firearms and don't require a license
E.G. a blunderbuss(flintlock shotgun) on sale online in Canada with no restrictions: https://www.thingsmilitary.com/long-arms/blunderbuss/
But quite frankly, that's even worse than a modern crossbow, aside from the noise factor, since flintlocks have an inherent chance to misfire. Putting it here for completeness.