One must be careful when discussing Arctic sovereignty issues, as it has multiple aspects:
1- There is the Arctic ocean itself, which is an ocean and thus recognised by all as international waters (if you can get there - or would want to for any reason).
2- Then, there is jurisdiction over the ressources of the Arctic seabed. Here the various countries contiguous to the Arctic coast are working within an international agreement at this time to map the continental shelves to effect a mutually agreed partition based on their findings. This may lead to some hard fought negotiations and long debates but it is not in itself a sovereignty issue any more than the Exclusive Economic Zones of 200 NM surrounding the waters of a country currently granted any sovereignty past the 12 NM national waters of such countries.
3- Then also, the limited debates within some nations concerning sovereignty over some lands, such as the Danemark/Canada debate over title to Hans Island (lest it votes for Independence from both
)
4- Finally, there is the issue of the status of the North-West Passage (and the North-East one in Russia): On the one side, the US claiming they are international straights and thus, even though acknowledging Canadian sovereignty as appropriate over the waters, subject to the right of free innocent passage (which also exists BTW in the territorial waters of a country not otherwise classified as internal waters). On the other side, Canada claiming the waters within the Arctic Archipelago as internal waters (such as bays, the great lakes and the St-Lawrence estuary) and therefore subjet to the absolute sovereign whim of Canada.
While the submarine use of the Arctic ocean by US submarines is of no political concern to Canada and they are free to use such international waters, the only truly issue that matters to Canada is use by the US without permission of what we claim as internal waters: The waters enclosed
within the Arctic archipelago.
And there, the US has two problems. Firstly, on the technical side, it would be very daring for a captain to take a submarine through covertly under water as the passage is quite shallow as far as submarine ops are concernend. It would even be reckless if done in winter when ice covered. Secondly, any covert passage would ruin the US claim of the right of innocent passage, which can only be exercised by a submarine running surfaced, while other transits - covert - would neither assist their claim nor qualify as innocent in law.
This is why I am not too worried at this point about US submarine ops, as I very much doubt they use what we consider Canadian waters to carry out their political agenda. They very well may (for all I know) use Canadian waters covertly to take temporary refuge from storms, fix broken equipment quietly or any other such reasons, but such use would be related to military purposes on which, we are on the same side, not political ones relating to our mutual debate over sovereignty of the Arctic.