Actually, if you use some waterproof carpenter's white glue, such as Titebond, the glue strength will exceed that of the wood. Glue, Clamp, let sit overnight, seal edges so that water does not creep in and swell wood and crack in a slightly different place, and you are good to go.

If at all possible, try to add a dowel or something to reinforce an area like the wrist of the grip. That gives you some grain running in a different direction which helps to reinforce the joint.

Good luck!