Having trouble with trapping.

[PALU]

Yes, rock throwing uses the Club skill. Throwing other weapons is supposed to use the corresponding weapon skill, although I've never investigated if you can train the Sword skill by throwing swords (spear throwing is a "legitimate" weapon attack, and I've done that to hurt animals).
I suspect throwing non weapon objects would be using the Club skill. It could use the general skill, but that would give you a bit too good a chance to hit (I believe the general skill is fixed at about 50%.

However, I didn't throw the rock. Once the elk is totally exhausted I catch up with it and whack it in the head with the rock using melee attacks (i.e. I aim for the head, but many blows end up landing elsewhere until it goes unconscious, at which time the hits are guaranteed to hit the intended target).

The reason for using a rock is that it causes the least damage to the skin. Also, throwing rocks at birds can occasionally knock one out so you can run up to it and kill it. That's been a (meager) supplement for many of my starting characters. This means the Club skill is useful to train. When I get further I mainly switch to a javelin and then to a spear (using blunt attacks in melee against non hostile opponents in order to preserve the skin. It also doesn't hurt that killing the target that way requires more attacks, and thus more training).