Etymology of "the C--- word"

The Oxford University Press blog addresses this word in a forthright manner:

By way of introduction, I should note that, judging by the examples in the OED, the English C-word was not offensive or at least not always offensive in Middle English.  No combination of sounds appeals to our prurient instincts because of their intrinsic qualities.  To shock or make us blush, they need a certain attitude on our part...

...there are innumerable descriptive and playful names for the genitals.  Is our C**t one of them?  I have looked at Classical Greek, Elizabethan, Modern German, and American students’ names for “vagina, vulva” and compared them with a list collected from the Samoyeds, a Ural-Altaic people inhabiting the tundra lands of the north, and another list from Italian dialects, that is, words used by people having minimal contact with book culture...

The next part goes beneath the fold -

The most common words for “vagina” in the Germanic languages sound approximately like put, fut, and kut ~ kunt (u frequently alternates with o in them).  An unsolved question is whether they are in any way connected, that is, whether we are dealing with some sort of rhyming slang, taboo, or even variants of fuzzy-muzzy.  As a rule, they are looked upon as three independent words, each of which needs an etymology...

I gravitate toward the conclusion that Germanic kunt is indeed a nasalized variant of kut (because of taboo or for expressive purposes).  Given this etymology, kin, along with Latin cunnus, fades out of the picture.  The origin of cut ~ kut may not be too obscure.  It is probably related to Engl. cot (cottage is the same word with a French suffix added).  Dutch kot means “sheep pen; dog kennel; pigsty,” and the English dovecote (which should not be fluttered) belongs with them.  Obviously, we have here the name of an animal house, an enclosure or some elevation above the ground.  If so, our word may once have meant “hole” or “little house,” both being among the most common designations for “vagina” in various languages...

You can fill in the ellipses at OUP.