Hi Sam:
Generally speaking, customs authorities in fully developed countries (North America, Europe, Australia & New Zealand, etc.) have no interest at all in vehicles being shipped out of the country - they have no reason to be interested.
It is possible that a random check might be carried out to determine if the vehicle has been stolen, but that is unlikely.
I have shipped my motorcycle back and forth between Canada & Europe several times - the customs officials at each end always look at the paperwork when the moto is arriving, but have never had any involvement when the moto is departing.
Be aware that ground handling costs (port charges at destination) vary considerably from country to country. I don't have recent experience, but in the past, the UK & Switzerland were kind of expensive, and France & Germany were less expensive. So do inquire about port charges when you make your arrangements. Anticipate that even in a best-case situation, you will probably have to pay about $150 USD to the warehouse that handles the incoming shipment.
Lastly, be aware that the incoming port will charge you storage on a daily basis. This can be very expensive because of the cubic size of the motorcycle. So plan to be at your destination to pick up the motorcycle the same day that it arrives (you will get dinged for one day of storage, even if the moto is only in the warehouse for an hour).
Lastly, although it is not "officially" necessary, it is a good idea to have your European insurance certificate (the "green card") with you when you go to the customs office to clear the motorcycle out of customs. You can't legally ride it without insurance. In theory, you could clear it out of the warehouse & leave it in the warehouse parking lot without insurance... but if you have the green card with you when you go to customs, it tells the customs folks that you know what you are doing, and makes it more likely that they will just stamp the papers and send you back to the warehouse without needing to make a visual inspection of the motorcycle before releasing it.
Michael
PS: In past years, Air Canada has run promotions to ship motorcycles back and forth between Canada & Europe. You can buy a seat on the same flight as your moto, and just take a taxi from the destination airport to the freight handler on the other side of the runway (no, the motorcycle does not come down the baggage chute like a suitcase).
Here's a link to Air Canada's motorcycle shipping page:
Air Canada - Fly Your Bike. They usually put up the details for each year around March or April. I'm pretty sure they will be offering very attractive deals during the summer of 2021.