January 13, 1832, Elizabeth Barrett Browning published a poem she called "The Pestilence" in The Times (London, paywalled). In it, she describes cholera as "the cold blue death". Among the US papers and magazines that soon reprinted "The Pestilence" was the Philadelphia Album of 21 Apr 1832.
Those, 13 Jan and 21 Apr 1832, are the earliest uses I have found of 'blue death' in the sense of "death from cholera", in the UK and US respectively. In a Lancaster Examiner (Lancaster, Pennsylvania; paywalled) article published 28 Jun 1832, titled "The Cholera", James B. Kirk, MD, observes
Blueness has been said generally to characterize this stage [of cholera]; but in this country that is not the fact. The skin of the hands and face is brownish, not blue.
Aside from occasional reprintings of Browning's "The Pestilence", the next use of 'blue death' to mean "cholera death" in the US seems to have been in the Nov 1849 edition of The Ladies Repository, in a piece called "Fugitive Letters", by Vindex:
The cholera's blue death, the thirst, the famine, and the scalping knife, will meet them on the way, and thin their ranks.
Use of the term 'blue death' in the relevant sense in US publications next appears in early October, 1867. The Evening Star (Washington, District of Columbia, p 1 col 7) of 03 Oct 1867 reprints what was to become a widely reprinted blurb from the New York Post:
It is curious to note the distinctions of color as applied to disease. There are the yellow fever, the black vomit, the green sickness, the white swelling, the scarlet fever, the yellow jaundice, and, as Mrs. Partington says, the "brown creeters." And now we have, as climax, the "blue death," on board the hospital ship at quarantine.
I found no further evidence of 'blue death' in the sense of "cholera death" in US publications through the later decades of the nineteenth century, and no evidence at all of any use of the expletive "Blue Death!", derived from French mortbleu, connected with death by cholera.
About The Blue Death, by Dr. Robert D. Morris: digitized versions of the 2007 hardcover and 2008 softcover editions are available at Internet Archive for free checkout (after registration).