Recoil Absorber
The person who mentions the recoil absorber brings up a good point: a recoil absorber is a spring type device that absorbs recoil energy as it compresses. An important thing to undertsand is that the recoil absorber does not reduce the amount of recoil energy directed into the mount of the gun turret (ie, the ship) by even one iota. That energy is conserved. What a recoil absorber does for any gun is spread out the time over which the recoil impulse is applied to the "mount". For handguns, that is your hand. For a battleship, that's the deck.
People would feel much less "shock" through their feet from the deck at fire with a recoil absorber because the peak of the pulse is lower in amplitude.
As to the ships reactive motion in the water as a result of the recoil (and Newton's Law of motion), would a recoil absorber change the distance it moved? No. The water applies variable resistance based on how fast you try to move through it (try it with your hand in the bathtub). So a sudden sharp pulse gets more resistance, the longer rolling pulse from the effect of the recoil absorber gets less resistance but over a longer time. So, the final amount the ship moves as result would be the same.. although, we have already established it would be quite small.