May suggest that as a temporary solution we really don't need realism. Putting a saddle on a horse doesn't automatically tame it IRL, nor does whistling as in other games. But at least those are solutions for gaining control of the animal npc and don't require new animations. Singleplayers aren't very concerned with animations (admittedly).
Picking up a small animal and having it just appear in inventory would be fine also. Then we can place it like any other object when we get to our enclosure.
A mechanism for herding other kinds of animals, goats, sheep, pigs, cows similar to the whistle method could be employed if you wanted something semi-realistic. And it would use the walking animations already in the game. You could point at the critter and issue the "you're tamed" command and voila it's yours. Though I suppose you could have some other hoops for us to jump through first.