The method used often depends on the design of the particular action involved.
Tig welding the hook, to build it up, is a method which is usually used on actions which have an integral hinge pin, like the Webley for example.
Webley DR actions have their hinge pin machined as part of the action frame and therefore it cannot be replaced with an oversize pin.
The original method with this style of action, before Tig welding was available, was to dovetail a piece of steel into the hook.

Personally, on an action which has a removable hinge pin, I would rather leave the hook alone, and instead machine a new oversize pin.