Canada will allow you to take a handgun in, but only under very limited circumstances, and what you are going to do isn't one of them.
A registered target shooting event, and you registered, and copies of your corespondence with the match organizers, and the gun registered in Canada, and carried in a locked case, OR to a cultural event that the handgun is required, with lots of documentation to support the situation.
If you try to take it and declare it, they keep it, and it's destroyed.
IF you take it and don't declare it, and are caught, you will lose your vehicle, all that you have with you, and may do time in a Canadian prison. They have a notoriously poor sense of humor regarding handguns, particularly when they are attempted to be smuggled in.
You can legally send the gun by common carrier (UPS or Fed-Ex) from yourself, to yourself, in Alaska in care of a third person, but the third person is not allowed to open the package.
Long guns are allowed to be taken into canada, but not anything military looking. A model 12 Winchester shotgun, with barrel cut to 20", takes down into a short package, and gives you something legal and compact for bear protection.
Do not even joke about having a gun for protection from people, that isn't a legitimate reason to have a gun in Canada. Protection from wild animals is, however.
I've been thru several times. I think it's worth the trouble. It's absolutely spectacular country to drive thru, especially Banff and Jasper parks, and the Alaska Highway. I'm going to do the Cassiar next time. Play it their way, and have fun, but it's their country, and they make the rules. They don't like it when visitors don't play by the home rules.
If you send your handgun around, keep your shipping papers with you. They may ask if you OWN any handguns, (they did me every time), then they will ask where they are. I showed them my shipping receipt, and my long guns (they wanted to see that they were not evil semi-autos, and were unloaded), and they were happy. Long guns have to be registered in Canada also, it's easy, but costs $50 to do. You can download the paperwork from the Canadian govt site.