Here is an Ngram chart for the years 1800–2000, tracking the relative frequency of instances of "one women" (blue line) and "many woman" (red line):
The trend looks positively alarming, until you match instances of "one women" (blue line) and "one woman" (red line):
It's true that the numbers for "one women" still aren't quite flatlining at zero percent, but the difference in frequency between that oddball spelling and the truly common "one woman" should be at least somewhat reassuring.
Further solace may be gleaned from the fact that Google Books search results very significantly overstate the typo problem, in several ways. For example, the Google Books scanner reads the phrase "twenty-one women" as an instance of "one women" because it doesn't know how to interpret hyphens properly: Reading hyphens as alphanumeric characters would lead to reports of hundreds of thousands of hyphenated words where there are really only word breaks between syllables at the end of lines of text. So the OCR scanner reads end-of-line hyphens as signals to close up the word straddling the line break, and it replaces hyphens that appear in the midst of lines of text with line spaces, which renders "twenty-one women" as "twenty one women"—a match for "one women."
Similarly, hyphenated compounds in which "women" is the first element lose their hyphen and sometimes produce false positives. For example, a Google Books scan of the sentences (from an 1808 magazine article)
Over this [room in Salisbury Gaol] are two rooms (to which the ascent is by a stone stair case from the court-yard) set apart for infirmaries ; they also have fire-places, but were equally dirty as the former, and filled with lumber. In the smaller one women-debtors are confined.
interprets the second sentence as providing a match for "one women."
Another major source of false alarms involves abutting sentences in which the first ends with one and the second begins with Women. For example, from Scott & Scott, One Half the People: The Fight for Woman Suffrage (1982),
The line of argument is a familiar one. Women have not succeeded in cleaning up politics, reforming society or ending wars, therefore suffrage is a failure.
Google Books again finds a match for "one women."
And again, when the one is bound to an earlier phrase of the same sentence—as in the case of this sentence from Myres, Westering Women and the Frontier Experience, 1800–1915 (1982):
On those frontiers where men outnumbered women by ratios of five or six to one, women often lived for months without seeing another woman.
—"one women" is reported once more.
Then there are instances where a section number leads into a section title, and Google Books doesn't see the break, as in this instance from Wemple, Women in Frankish Society (1981):
Women in Secular Life
Apostrophes pose another problem. Google's OCR scanner reads both this instance (from 1985)
One of the requirements of manhood in Bahia was that one be able to protect and control one's women.
and this one (also from 1985)
Only one women's service magazine does not accept cigarette advertising in the United States.
as matches for "one women."
There are even some instances where the Google OCR scanner does everything right, and finds and reports an instance of "one women" involving no intervening punctuation marks, and yet the occurrence turns out to be grammatically correct anyway—as in this case from Rowe, Women's Issues (1986):
It's a simple question, and one women often easily overlook.
As a result of all of these complicating factors, a large majority of the Google Books matches for "one women" are not typos for "one woman" at all, as you can confirm for yourself by scrolling through some of the "Search in Google Books" listings beneath the Ngram viewer graph for "one women" vs. "many woman."
That's not to say that instances of "one women" as a typo aren't increasing in published work: They are, especially as copy editors and proofreaders leave the industry in cost-cutting moves at more and more publishing houses. But the scope of the problem is easy to exaggerate; and at least for the time being, "one women" does not appear to be on a path to legitimacy as a straight-up alternative to "one woman."