That's probably a question better put to one of the better known gunsmiths, as most all have GTAW capabilities. I presume you're refering to the dolls head fit.
What I would be most concerned with is keeping the heat input to a minimum, with quick arcs, since the ribs are soft soldered to the barrels. Additionally, he might use heat sinking materials wrapped in the area to absorb the heat. It might be better done removed, and then reattached prior to file fitting. My experience with welding processes is extensive, but far removed from this, a more delicate detail than steel components we made. Welding is often more than simply joining two pieces of ferrous metals. It can, and often is used to correct machining errors. Two $70,000 steam turbine diffuser diaphragms we made we over machined, by a mere .005", at the joints, which wasn't detected until they were completely fitted into the turbine. The rotor was lifted out, the joint faces were 'buttered' by GMAW, and the entire turbine cases were put on a planer mill ( Table was 12'x80') and milled back down till they were kissing the joint face. High temp ceramic blanket stress relief for PWHT. Even though it was GE's error, I didn't want to have to make them over again.
If you know anyone over in Newport at Ruger you might get into Pine Tree Casting; their investment casting foundry, on the property of the gun company. Pine tree is a substantially captive operation, making investment castings for the gun manufacturing, though they do outside work also. All the Vaquero parts, right down to the triggers, are investment castings, and they do in-house, cosmetic TIG on the many parts which have small surface defects.
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