Why laughable? Inoculation was done in that part of Africa. Other diseases will probably be a problem though...
Smallpox was only eradicated 40 years ago through the a major worldwide effort relying on modern medicine, production, and logistics. It is arguably one of the greatest accomplishments of humanity.
If inoculation (variolation) could stop (rather than lessen) the spread of smallpox none of that would have been necessary. Keep in mind that the last cases of smallpox were in the Horn of Africa. Again, if inoculation can stop smallpox, why are the last known cases in an area where the knowledge of inoculation was available for centuries?
The largest problem as I see it is that variolation requires an active virus. You take the active virus from an infected person and transfer it to another person. (It can be preserved briefly and unreliably.) That simply can not be contained with the technology of the day. At some point, the virus is going to be accidentally spread. Once it is loose in the Americas, it will spread uncontrollably.
For the sake of this working, that can't happen.
Which makes the scenario unlikely. It's fine for storytelling, but does not make believable AH.