First off, I do not want to offend anyone. Secondly, I am not a gunsmith, nor do I play one on TV. However, I am a trained machinist and an engineering student. I have both formal training and hands on experience, so don't give me any nonsense about sitting behind a desk. I have paid my college tuition with what I earn working in a machine shop.
That being said, the comments regarding safety are certainly logical. As you all know, when you fire a round, the cartridge case pushes back on the frame. If the force that is exerted on the frame is not resolved, the gun will fly apart. That is why the barrel/frame lockup is important. In the case of the Handi, when force is exerted on the frame's breech face, the pivot pin exerts the same force on the barrel under lug. Because the forward thrust on the barrel is the same as the backward thrust on the under lug, the forces are resolved and things stay together, as long as the under lug is securely attached to the barrel. If the barrel is not securely attached to the under lug, things come apart because the forces cannot be resolved.
In the case of a stubbed barrel, the stub effectively functions as an under lug, so the barrel blank must be attached securely to the stub. Basically, when you shoot, the force tries to pull the barrel blank out of the stub.
Another example: In most common bolt action rifles the barrel is threaded to the receiver. Those threads are what ultimately bear the load. The locking lugs merely transfer the force from the bolt to the receiver. Properly cut threads are surprisingly strong.
As far as this goes, well, you can make up your own mind, but think of it this way: With a .357 running at about 35ksi, you have about 3500 lbs of force trying to pull the barrel and stub apart, according to the formulas Tim posted above (those formulas are actually simplified, but they are a good approximation). It's up to you whether you feel that whatever method you used is good enough. My personal opinion, which by the way is based on fundamental engineering principals such as statics, dynamics, and mechanics of materials, is that this method is POTENTIALLY unsafe and I would not recommend it.