Obviously, I would have no qualms about using Titebond II. It is a proven performer in clean walnut. In some circumstances, I would choose a good epoxy, such as if there was any amount of gap filling or if I needed to glue in reinforcing pins. I have never used cyanoacrylate glue to repair a gunstock. They may have their place to stabilize rotted punky wood that had been oil soaked, but it is not strong in a shear condition, which is the type of stress that breaks toes or knocks off a piece of wood behind an action or tang. Certainly not for a broken wrist.
This opinion may change when I get a chance to try Titebond III.