Nope, its an export even if it just leaves the U.S. for a minute. The Canadian requirements have to do with their import policies, not the U.S. export regulations.
The Commerce Dept. and State Department regulations even cover movement through one country on the way to another. And sending parts for firearms requires a license as well. These are defined as "defense articles" under the International Traffic in Arms Regulations ("ITAR"). Any movement out of the U.S. is an export, either a permanent export or a temporary export and if it is a defense article it requires a license from the Directorate of Defense Trade Controls which requires that you be registered first with the DDTC. A shotgun with a barrel over 18" is specifically exempted. Nigh vision and "military" rifle scopes are regulated as well. Cabelas paid a $680,000 fine for exporting those without a license.
http://www.exportlawblog.com/archives/425