If the target creature is an illegal target by the time Master of the Wild Hunt's ability tries to resolve, the ability doesn't resolve. You won't tap your Wolves, and nothing will deal or be dealt damage.

Only a Wolf creature tapped as part of the ability's effect can be dealt damage by the target creature.

The controller of the target creature doesn't divide that creature's damage as the ability is activated (since the Wolves that will receive that damage aren't targeted), so that player does so as the ability resolves. There is no time to react between the time a Wolf is chosen, the time damage is dealt to it, and the time it's destroyed for having been dealt lethal damage. If you want to put a regeneration shield on one of those Wolves, or target it with a damage-prevention spell, or anything else, you must do so before the ability resolves (and before you know which Wolves will be chosen and how much damage will be dealt to them).

All Wolves you control are tapped as part of the activated ability's effect, not as a cost. Players may respond by attempting to tap or untap Wolves, or to create or remove them.