By creating a shallow cavity on the backside and laying in a metal or wood "stiffener" (filler that adds strength), you won't have to disturb the outside surface. Doing it shy of "full length", it would definitely stay hidden.
Setup would be like Hawg (hey Hawgie!!) suggests which would give you a solid piece. Carefully inletting a shallow recess and epoxying the stiffener in place would complete the repair.
Mike