Looking at a Winchester from the 1890s that has had the tang welded back on after being broken. I'll assume the work was good, but are there issues with mixing modern welding with steel over 100 years old?
I wouldn't worry too much about it on the tang, but if they welded anywhere near the chamber I would recommend having it checked by someone qualified to assess the heat treatment.
If you are going to shoot it I would have a welder look at it. Even have it Magnafluxed to be safe. Why guess. Can it be safely welded, most likely. But is will most certainly need to be stress relieved when it's done.
^This^
From my limited understanding of metallurgy, you're half right OP. It's not so much the 100 year old metal but the conditions it's been in and type of alloy. Things like hitches and plow mounts can have issues with hydrogen cracking from being exposed to the elements. IE weld it, use it, it breaks from the metal coming unzipped right along the weld OR the alloy of the filler metal or added bits being the wrong hardness/brittleness/melleability and not dealing with the shock load of firing the weapon. I wouldn't go at it with my garage welder but maybe the tig at work if I weren't too concerned with the longevity/use. If I wanted it fixed to original or better I'd talk to a gunsmith who does such repairs.