Find a local welder who is good with TIG. Have them run a fine bead or fusion weld it (no filler rod). Then file it down, polish, and refinish it.
SP is right and it is not structural, so deap penetration is not needed on the weld. Just make sure it is as clean as you can make it before you hand it over to the welder. Heck if you were in the NW I would do it for beer!