With climate change there is a renewed interest in the NWP. Most boats up there are, I suspect, government research vessels and icebreakers (check Canadian Dep't of Fisheries and Oceans) and some boats that shuttle goods to coastal communities. Keep in mind that the navigational window is only a couple of months. I am aware of 2 people who did it by kayak over 2 years but that is a whole other undertaking! I would suggest browsing websites for the Yukon, Northwest Territories and Nunavut for leads to shipping companies and crewing opportunities. Local papers would be good to check out as well.
Pack a parka