The avionics have to change as well, as the change in airframe would be large enough to warrant a complete overhaul of the FBW system. Basically, the plane would be almost as different from the J-10A as a J-11 with the same radar. It would be a whole new plane, and I don't think it's worth the trouble. A combination of J-15 and L-15 would probably work better for carrier operations. The L-15 is already equipped with PESA radar and afterburning engines, giving it a 1.0+ T:W ratio with normal equipment.
IMO, the L-15 is designed with carrier options in mind, or else it'd be sort of a waste of resources to have both the JL-9 and the L-15, especially when the L-15 costs about as much as a JF-17. The L-15 will first serve as carrier operation trainers and then there should be single seat variants serving as point defense fighters. A twin-engined, highly maneuverable fighter capable of firing BVR missiles is nothing to scoff at.