I would not recommend using screws at all, it will not gain any additional durability and the technique would be more in the realm of a "bubba" repair. If you have the tools and skills necessary, a traditional dowel and glue repair would be best, and if done properly will definitely enhance the resale value, versus the screw option, and is the same type of repair that would have been performed by an armorer in the field or at armory.
I will use wood dowel, for the brass screws my first idea was to hide them, you drill a hole just big enough to hide the screw head.