[Raynor]

But this, I think, substitutes a greater problem for a lesser one: if he was not human, what in Arda was he?

Tolkien did attest he was human:

Originally Posted by Letter #144

Beorn is dead. He appeared in The Hobbit. It was then the year Third Age 2940. We are now in the years 3018-19 . Though a skin-changer and no doubt a bit of a magician, Beorn was a Man.

The question is, was he a pure man? Or did he have some other influence in his blood, which would validate his magic?

The second example is that of the Druedain. That this people is in the possession of some kind of magical skill is quite evident from the essay on them in UT and, particularly, from the story of 'The Faithful Stone' told there.

Well, that could be chalked up to heresay; moreover, the drugs were supposed to go to Numenor, and were eligible for the gifts of Eonwe, power, life and knowledge. Who knows, maybe Eonwe didn't forget them and still gave them something.

When one adds these instances to the examples of the Mouth of Sauron's claim to be a sorcerer

It is said that the power of the two trees and the presence of the holy ones immensely increased the status of the elves; isn't it possible that the presence of Sauron, Melkor's greatest maia, the one who inherited a good deal of his power, could affect, in a somewhat similar manner, the status of the mouthie?

I think it becomes evident, or at least probable, that Men can in fact use magic.

I think the problem is not use of magic, but 'generating' it. Even the hobbits can wield the ring's powers to some extent, but none could make one; humans can look in Galadriel's mirror, they can see through the palantiri, they can "sense" the coming of orcs using elven blades, but they can produce magic, we never hear of such a thing from a "pure" human.