I hate to comment because Im a crappy welder but, I design welds all the time so I'll say something. I would approach this question from a different direction.
The most important factor is the stress the weld must withstand. First, make a reasonable estimation of the stress the weld will experience upon firing. Next, decide how comfortable one is with stressing a weld to that level. We will need to know the barrel wall thickness at the saw cut to estimate the stress.
For safety I would assume a high chamber pressure. Then I would consult one of those pressure drop diagrams and conservatively assume a pressure at the saw cut. Then I would calculate the resulting stress in the weld.
If the stress worked out to 5,000 psi, I wouldnt worry about not knowing the exact metallurgy of the barrels. If the weld stress was 30,000 psi I might think differently.
Anyway, first determine how good the weld needs to be. Then decide on the testing and welding procedures needed for peace of mind. The barrel wall thickness is important.
One thing working for this gun is that it is a small bore so the stress equation is more favorable for a given pressure.
