What is a myth is the "dumping all its energy" mantra. When you shoot a handgun, how much energy is dumped in your palm? A similar amount of energy is dumped into the target (physics) and it isn't enough to make any difference.
You'd be wrong. As per Isaac Newton: For every action, there is an equal and opposite reaction.
Kodiak, you're playing too strict with the laws of physics. You're treating the action of firing a gun as a static situation when its actually a dynamic situation.
First off, you need to understand that the bullet kinetic energy is not reacted into the gun, rather it is the force of rapid pressure change of the burning powder in the cartridge. When the primer is struck, it ignites the powder, which rapidly burns and changes into a gas. Using the combined gas law of PV=nrt to determine cartridge pressure, we can then set about figuring out the forces being translated into the frame of the gun and bullet.
Since pressure is defined as P=F/A, we look at the internal surface area of the cartridge and the surface area of the base of the bullet. Once these two are known, then we can determine forces acting on the cartridge and bullet. The forces inside the cartridge prior bullet release are symmetrical, equal amounts of force all around the cartridge. However, when the bullet is released the forces are asymmetrical, most of the force acts on the bullet and not on the gun.
As the bullet moves down the barrel, pressure is being reduced due to an increase in volume (as the bullet is displaced, gases take its place). The farther down the barrel the bullet goes, the less pressure there is acting on the gun. As the pressure is decreasing, the area for the pressure to act on is increasing which means the force is
decreasing. Since both pressure & area are square units, pressure decreases by a square root for each unit increase in area (a 1 unit increase in area results in a 4 unit decrease in pressure, a 2 unit increase in area means a 16 unit decrease in pressure, ect.). The progression of pressure reduction is not linear, its exponential. This results in an exponential reduction of force the farther down the barrel the bullet goes.
Once the bullet leaves the barrel, all the remaining pressure exits the muzzle following the path of least resistance since the primer was struck. The path of least resistance in the case of firing a gun for the cartridge gases is to push the bullet out of the gun.
Now onto recoil. Recall how the pressure goes from symmetrical to asymmetrical once the bullet is released, this defines the recoil you feel. To define the symmetrical pressure recoil force, you need to add another variable: time. The symmetrical pressure recoil force is F=PAλ. λ is the time that is experienced at that specific PA. Since λ in the case of symmetrical cartridge pressure is defined in pico-seconds (millionths of a second), the max recoil force attainable is extremely low. This is called a specific impulse. The forces during a specific impulse can be tremendous, but short time frames drastically reduce the actual force of the impulse. Also, the cartridge base that pushes against the firearm itself is exponentially bigger than the base of the bullet, which leads to lower force imparted on the frame of the firearm than the base of the bullet during the specific impulse. Once the cartridge pressure becomes asymmetrical, the force acting against the gun drops exponentially.
Now, to sort out kinetic energy vs recoil. Kinetic energy is F=ma. In the case of a firearm, a is acceleration with a given direction: velocity. Convert grains to pounds and multiply by muzzle velocity to get ft/lbs of kinetic energy. As for recoil, the specific impulse that acted upon the cartridge base is greater than the weight of the gun. Subtract out the weight of the gun in pounds and you get the actual recoil force in pounds. Since the body isn't a rigid structure, your hand & arm displace to absorb the small amount of force involved.
A gun is nothing more than a pressure vessel that controls the direction and release of pressure.
As for hydraulic shock, apply the same math plus the average speed of sound in flesh to determine the rate at which the bullet kinetic energy will be imparted, determine the λ for bullet/tissue interaction time and you get a good idea of how much hydraulic shock will be imparted by any given round.