I do believe the O.P. said the magic word: Antique!
To our O.P.: If you have your RCMP letter for it, that would help. FRT print with RCMP logo and such is second choice. Some document stating YOUR pistol is antique is ideal.
After that, it goes for a holiday in the USA by mail, no problem. It gets worked on, it comes back. No problem. It's an ash tray. It isn't a firearm, here or there. You simply need to ensure your shop will work on antiques, and will ship it back the same way it came.
Sorry, I won't give you my contact, I only have the one and he's busy enough as it is. But antique is the magic word -- just document properly, and declare it as "Pre-1899 Antique" going there, and "Pre-1898 Antique" coming back on the customs form. No need to say "Firearm" -- anyone who knows their business, knows the meaning of the words you wrote. The word "Firearm" translates to "Steal Me" in most major languages.
An antique broom handle is still a $5000 or $6000 proposition, even in poor cosmetic condition. I'm not sure what the limits of postal shipping insurance are, but that's probably close. And customs will definitely look if you insure the package at that value.
You may want to drive it down and pick it up again. It could be cheaper than mail with insurance. Just get clear on your obligations at the border first.
I have recently seen some lovely pictures of a Broomhandle Mauser sans barrel. The pistol was rebarreled by an Eastern gunsmith and both the bullet and barrel went downrange when the owner pulled the trigger. Find someone who knows what he's doing. Personally, if it is shootable as it is, I would get into reloading and forget the 9mm bit. In the woods, it is much deadlier to anything you encounter in its present (near .357) form. Excellent penetration and accuracy. As a mediocre 9mm, not exciting.
Best of luck with your project!