If you doubt your welding ability, then you can use simpler solder techniques to fix the tang.
A couple ways to do it.
First is to cut the tang completely off from the plug portion. Make the cut horizontal with the tang and at the lower/bottom edge
of the tang thru the plug portion. That leaves you with the breech plug w/no tang and a step on the top of the plug portion that is
as deep as the tang is thick.
Now make an entire new tang to the dimensions you need to cover any excess wood cuts in the stock, extra length you want, ect.
Make it extra large from that measurement to allow for a bit of final fitting and shaping.
Bend the new tang to the shape you need to have it before the next step.
Then attach this new tang to the breech plug at that 'step' you cut on the top of the plug.
Use "Hard Solder" (we called it Silver Solder, but that isn't PC anymore I guess). Hi Temp stuff,,1200F
Or Braze it together,,pretty much the same thing,,just a bit more heat and some better strength.
The Solder joint won't show as it's underneath the tang as viewed in the assembled pistol.
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Another way to fix it but using Soft Solder is to Half-Lap the existing tang with a new one. That joint can be soft soldered
and will be plenty strong.
Again cutting the existing tang down BUT NOT OFF.
File about half the thickness of the tang down along it's length,,or shorten the tang a bit to make the work easier.
I would cut the tang off completely just ahead of the off center screw hole to avoid all the work of fileing the entire length.
File the remaining portion down FLAT to about 1/2 the thickness of the orig tang. Less if it leaves the tang quite thin.
Make a new tang as in the above repair. This time on the underside of it file a matching flat on the front end of it
to mate with what remains of the old tang. Make the fit as close as possible including the small step in the two parts where they abut.
Use soft solder and sweat solder the two parts together.,,(or you can Hard Solder them together as above.)
An extremely strong joint and as above will not show the soldered joint on the assembled gun.