Lee Schierer in McKean, PA
If the broken part fits back in place with no gaps with finger pressure, I would use CA glue. Spray some activator on the beak and place a drop of CA on the bird. Carefully align and press the pieces together. You should get a near instant bond with no run out and no visible glue line.
Shellac use alcohol as a solvent so applying new shellac over the old should blend right in by partially softening the underlying layer of finish.