Skan, when one thinks of a unicorn, one thinks of a large horse-like animal with a long horn between its eyes.
Also, the hebrew word here is "re'em", whose best definition, according to a Jewish acquaintance, is "wild ox", or auroch. This is reinforced by Deut.33:17, which in the KJV refers to the horns of a unicorn.
As for the auroch, it was a kind of bovine related to modern cattle, only it could often reach over a ton in weight. It was a favorite prey of ancient hunters, and was hunted in Europe into the 17th century, the last known specimens being found in Poland in 1627, putting it very much into the range of knowledge of the AV writers.
Another candidate for re'em is the gaur, a large, wild, untamable ox of SE Asia & eastern India.
And I don't entirely disagree with the validity of your candidate, the Indian rhino.
And another possibility-some ancient warriors placed a protective mask about their horses' faces with a long, sharp spike between the eyes for a fierce appearance, and sometimes for actual use by a well-trained horse.(I can't remember the name for that spike!)
And the constellation 'monoceros' represents the horse-like unicorn.
But at any rate, the rendering "wild ox" in the MVs is certainly not wrong, especially in the light of what we perceive a unicorn to look like if it ever existed.