The word went from a botanical meaning in the late medieval era, to in the 18th century meaning near the modern sense, introducing disease agents to provide protection, and then in the mid-late 19th century a negative sense, meaning to infect, often through a wound. In the 1760s the negative sense (meaning to infect with the intention of killing not protecting) would be unusual.
The OED says in its entry on inoculation that the oldest sense was to propagate a plant by grafting it onto another plant's root or stalk. In the early 18th century this expanded to providing protection against smallpox and other diseases: "Originally applied, after 1700, to the intentional introduction of the virus of smallpox in order to induce a mild and local attack of the disease, and render the subject immune from future contagion; also, in 1799, to vaccine inoculation, afterwards called vaccination n.; and in 19th cent. to the similar treatment of other infectious or contagious diseases."
We can find many other examples: from a paper about the history of inoculation the word is used from the early 18th century when the British became aware of the ancient use of inoculation in the Ottoman Empire. From 1714: "The writer of this ingenious discourse observes, in the first place, that the Circassians, Georgians, and other Asiatics, have introduced this practice of procuring the smallpox by a sort of inoculation, for about the space of forty years, among the Turks and others at Constantinople." (The origins of inoculation, Arthur Boylston, J R Soc Med. 2012 Jul; 105(7): 309–313. doi: 10.1258/jrsm.2012.12k044) It appears likely that this meaning was extended from the older botanical sense.
From 1838 the OED also has the meaning of introducing infectious agents through a wound without intention to stimulate immunity, e.g. "Hydrophobia..is the disease occasioned by inoculation with the saliva of a rabid animal." (Quoted under "inoculation".)
It's interesting looking at the OED's entry for inoculate, which seems to somewhat misinterpret what is happening in its early citations: it gives from the 18th century a meaning: "3a To engraft or implant (a disease, or the germ or virus) upon an individual, by a process of inoculation n.; to introduce (cells or organisms to be cultured) into a culture medium or its container." But its example actually refers to early 18th century smallpox experiments, if we look at its first example from 1722. Its earliest example of "inoculate" to unambiguously mean to infect without intending to stimulate immunity is from the late 19th century: "A man with a scratch might inoculate the poisonous germ from contact with an infected animal." (Daily News, 1892) "Virulent anthrax bacilli are inoculated subcutaneously into an ordinary rabbit and into one that has been rendered immune." (A system of medicine, 1896) The last of these shows a medical source using it to mean to introduce pathogens into tissue.
It is possible that Amherst was using the word "inoculation" ironically (what is disease for the Natives is a cure for British problems), but I don't see any evidence of that.
(Note, there are subtle differences in medicine between variolation and inoculation and other terms, but I didn't attempt to differentiate here. You can consult a reference work for more information.)
Refs:
- "inoculate, v.". OED Online. December 2021. Oxford University Press
- "inoculation, n." OED Online. December 2021. Oxford University Press