Good luck finding a 4.25" super bearcat barrel in Canada. Super bearcats are not that common in Canada which is why it will be difficult to find a barrel domestically. Though more common in the US , the super bearcat didn't really catch on because the sight radius from a 4" barrel negates the little gain you get from a 22mag being shot though such a short barrel. Yes, there are gains but do the pluses out weigh the negatives and the answer is, no. There is no real improvement in accuracy, 22mag is a bit bulkied, large portion of the power charge is waisted from such a short barrel and the cost of 22mag is what, 5Xs or 6Xs that of 22lr!?!
If you plan to go the barrel reclassification route, I can almost assure you that you will be paying close to double that of a new bearcat in 22lr. Let me do some hypothetical math for you... you get the gun for (say) $200cad. Numrich has a SBC barrel for $350USD, $60 delivery and because a barrel is a controlled part of a firearm according to US law, you get go pay a $200 tax on it. 610USD into CAD, roughly 820. I don't know how much gunsmiths rates are but lets say $200 for the barrel exchange and paper work. So conservatively you will be into it for roughly 1220. A new Bearcat in 22lr is around 710. I picked up a used minty stainless steel one for 350 in a private sale over the winter just to give you an idea of the used market prices.
Don't get me wrong, I love the bearcat and have several in my collection and I love the 22mag for what it is but i my opinion, the combination of the two is not worth the time and energy and defiantly not worth paying twice as much for a used gun. The 22mag is unquestionably first and foremost a rifle round and is most effective as one. Get a 22lr verson would be my suggestion. If you are just considering it because of the size, there are smaller and lighter guns in the restricted category. The 1911-22 comes to mind. And if you want more power which is why you are considerring the 22mag, get the 1911-380ACP black label in a polymer frame. These are 85% the size of a 1911 and even with the 4.25 barrel, they are small. Some times when I am recognizing my vault, I slip my 1911-380 into my front pocket so that I can carry my guns from one shelf to another and to be honest, i really don't know how these are not prohibited. They are smaller and lighter than some of my prohibs. Black labels are around 900 and you can find 22s for under 600 and the grip is smaller than a bearcat. But if you really have to have a bearcat in 22mag...
. Easier for me to grip. Right now barrel is 102mm, 10.2 cm, 4 inches, 36 thousand whatchamacallit. Etc. 
