Lightly sand only the bottom, to remove a bit more of the old finish and even out the color, then apply Teak oil or Tung oil, which will penetrate the wood. The oil will repel moisture, but it isn't truly waterproof. There may still be some mottling of the finish where the oil doesn't penetrate the old finish.
For a more waterproof finish, do the light sand and use spar urethane (polyurethane) . It will dry to a hard finish similar to the rest of the stocks, but may not match the color exactly (neither will the oil finish). Careful not to overlap the edges or you'll have a "ring" at the bottom of the grip sides, and don't get any inside the grip halves.