Get official information from the Canadian Govt about exporting weapons and find out officially if a wooden bow is even considered a weapon under the law. Do the same for the US. I can't think of any country offhand where a bow is illegal to own(unless it was a crossbow, some countries class them as prohibited weapons)
I would be surprised if it is actually even legally considered a weapon, and not sporting tackle. Don't rely on a website, get actual clarification from an official, in writing. Email the official correspondence to the shippers.
Many people that work at these places are ignorant of the law, and just make it up on the spot. So if you can show them they are factually incorrect, and that it is okay, they will ship. They are only worried about complications, and a potential lawsuit.
Likewise, I'd be very surprised if they can destroy a parcel without, first informing you, and giving you the chance to appeal the decision, at the very worst it should be returned to you, the sender.