I wouldn't worry about the barrel of the OP's gun. It is steel, not twist, and the weight of a 12ga. is governed by recoil. A double may be as thin as will resist accidental denting, but a single is likely to be thicker in the walls. The underlug is also forged integrally with the barrel, eliminating the possibility of the steel being impaired by brazing. You should be able to do it without "burning" the steel, and the introduction of marginally lower-temperature silver solder in the 1940s reduced the likelihood still further. But it can happen, and short of polishing an area and using a microscope to do some very expert examination of the grain structure, there is no easy way to find out.
There might be some more doubt about the receiver. It is probably steel, and safe with conventional smokeless loads, but how do you like the sound of "probably"? Some early ones may have been made of malleable cast iron, as I believe the Stevens Favorite .22 was. Most of the common Belgian .41os are good for smokeless, but I have seen a very old one with an open crack running down from the bottom of the breech face, and I am sure that that one was iron.
You could drill into some hidden and non-weakening part of the receiver, such as the web into which the stock drawbolt screws, with a drill of about a sixteenth of an inch diameter. If it produces a curly, wiry shaving with some strength in it, it is steel. But if the metal exits in short chips, particularly dark ones, it is iron.
Here is a crossover list of store brands, as ppublished in an old Numrich printed catalogue. It will sometimes be of help, although not this time. It simply shows some store brands as being made by Springfield.
www.nramuseum.org/media/940938/store brand crossover list.pdf