Again: it's not about the islands, it's about the water between them.
Let's stipulate that Canada owns every island in the hemisphere. Now what? If enough ice melts that there's a passage between them which doesn't come within 12 nautical miles of an island's coast, then there's a passage that isn't in Canada's territorial waters, and Canada can't, under current international law, forbid ships using the passage.
For the passage in the wikipedia diagram, both of the two paths after the first bifurcation (moving westward) pass through channels less than 24 nautical miles wide. Canada would need to build observation towers but it could be defended with "cannons" e.g. the M777.
Let's stipulate that Canada owns every island in the hemisphere. Now what? If enough ice melts that there's a passage between them which doesn't come within 12 nautical miles of an island's coast, then there's a passage that isn't in Canada's territorial waters, and Canada can't, under current international law, forbid ships using the passage.