Except for the 685 all 680 series barrels are interchangeable, some fitting may be required. Where the major issues are is in the rib height, so your comb height may need to be adjusted to match the rib height. So, for example, your current gun may have a flat rib barrel and your comb is set up for that barrel configuration. If you buy a step rib trap barrel, your comb would have to be raised or you will be looking at the back of the rib.
It is against US law to export firearms or parts, like receivers, barrels, trigger assemblies, etc. without an export permit. Miscellaneous parts can be exported up to a value of $100 without a permit. Most gun dealers won't sell to Canadians as it would jeopardized their firearms licence. They can tell you are Canadian from your credit card, so don't try and buy it and have it sent to another address. A US citizen that buys it for you is also in jeopardy. Having said that, it is unlikely that you will get caught. The Canadian government only cares that a firearm or receiver is registered, but mainly they want the tax.
Many American individuals will sell you a barrel and ship it. Most don't know that that is against their law and some don't care. If you purchase one in this manner and have it shipped here, make sure they don't put gun barrel on the customs declaration. Machined part works well.
Joel Etchen has probably the best selection of Beretta barrels. Here is a link to his web site
http://www.joeletchenguns.com/ Another good place to buy barrels is on the discussion forums on Trapshooters.com
http://www.trapshooters.com/
Good luck.
PS: Prophet River Firearms can import a barrel for you.