Short answer: inoculation.

The British in North America didn't need germ theory to see that when someone without smallpox hangs around someone with smallpox, both people get the disease. Inoculation, the precursor to vaccination, was known to Europeans by 1670 and was based on just that fact: unlike the smallpox vaccine, which was an injection of cowpox, inoculation involved actually rubbing a live smallpox scab, or pus from an infected person, on the skin or open wound of a healthy person. The hope was that the healthy person would develop a localized, less severe case of smallpox, and when it was all over, they would be forever immune. Because the inoculated person would still have to get smallpox, and would still be contagious for a while, this was a fairly controversial practice. Either way, people understood that you could rub smallpox on another person, and the other person would get it.

So, in 1763, the British were fresh off a victory over France in the Seven Years War, but the Native American tribes-- who had allied with the French-- continued to fight the British. One garrison, in particular, was under siege by the Delaware and Shawnee tribes: Fort Pitt, located in the Ohio River Valley. On June 23, Colonel Henry Bouquet, field commander for NY and PA, wrote to Sir Jeffrey Amherst that smallpox had broken out in Fort Pitt the previous week. Amherst wrote back on July 7 that "could it not be contrived to send the smallpox among those disaffected tribes of Indians?" Bouquet wrote back that he would try "to inoculate [them] with some blankets that may fall into their hands, and take care not to get the disease myself." Amherst agreed, writing that "you will do well to inoculate the Indians, by means of blankets, as well as to try every other method, that can serve to extirpate this execrable race." Emphasis mine. The word used here is inoculation. Amherst and Bouquet are talking about using an already common medical technology for the purpose of infection, not prevention.

(But I want to add that Amherst and Bouquet never actually followed up on the plan, because somebody else had already done it for them. On the night of June 24, William Trent, owner of the fort's trading post, wrote in his journal that "we gave them two blankets and a handkerchief out of the smallpox hospital. I hope it will have the desired effect." When Trent sent a bill to British gov't for expenses incurred during the siege, he specifically marked a charge for the blankets and handkerchiefs, "taken from people in the hospital to convey the smallpox to the Idnians." This bill was certified by Captain Simeon Ecuyer, captain of the Fort Pitt garrison-- while his involvement with the plan is unknown, the fact that he approved the expenses on the bill suggests that he had known of it.)

Source: Jones, David S. Rationalizing Epidemics: Meanings and Uses of American Indian Mortality since 1600. Harvard University Press, 2004, chs. 3-4.