Velocity and energy are definitely related. How much energy there is to potentially transfer is dependent upon the velocity and mass of the bullet.
Yes, the size of the frontal area, as well as the pressure put on the bullet and animal, and this how the bullet reacts and deforms will determine how much or how little energy is transferred and how much of a shockwave is produced.
A smaller caliber, longer, more secant bullet with a small meplat, and that is constructed in a way that resists expansion will not produce much of a shockwave, if at all, compared to a larger caliber, softer constructed, and with a wide meplat bullet.
How much hydrostatic shock is produced is just as much tied to the construction and terminal behavior of the bullet as hydraulic shock. Hydrostatic does require the bullet to at least impact at supersonic speeds though, whereas hydraulic shock can still occur at lower speeds.