You might be able to find someone who is an excellent TIG welder who can add the needed metal, and can machine it down evenly to fit well, but personally I have never found anyone able to do the job to my satisfaction, and I have seen a lot of skilled guys try (I do a lot of TIG welding and machine work, using milling machine/lathe, etc. too, and I can't do it to my own satisfaction either). The main problem I have found, is that it is extremely difficult to add the necessary metal AND to machine it square all the way across the hook, so that it bears equally, evenly, across the hinge pin surface. If not done well, it will wear way more quickly than ever before. On the other hand, I have found it way easier to install an oversized pin to take up the wear (on some doubles that have an easily changed pin), or to dovetail in a shim to the hook, a shim that may be easily replaced any time in the future as well (I use methods for this, as explained by W. Ellis Brown in his book, Building Double Rifles on Shotgun Actions, a method borrowed, I think, from a great English gunsmith).
This method was developed to take up wear on British doubles that have a hinge "pin" that is machined as a part of the overall action body, so isn't really a pin at all, making it impossible to change the hinge pin unless one drills out the area that functions as a "pin," and installs a whole new one.