Why do you think you would need a handgun? Have you ever shot a bear? They aren't that hard to kill. Do you think you could hit a bear with a pistol if you blew the shot with a rifle? Not sure I understand the mindset of dragging a handgun across the international border. What does your outfitter have to say about it? If you're an American and I'm assuming you are then by law you have to hire a guide in Canada. I'd be sure to get the outfitter's take before I did any paperwork.
But, to each his own.