Huh, I didn't know the smallpox vaccine came about that early.

Either way, there were still plenty of nasty diseases from the Old World that had (or still have) no vaccines, like cholera, typhus, typhoid, measles, malaria, influenza, leprosy and bubonic plague. Their cumulative effect sapped native societies of their vigor, and this would have persisted even if they adopted the kind of sanitation technologies that Euros brought.

The reason it took Europeans until the 19th century to conquer the African interior was that disease was so difficult to overcome. Until quinine was developed, the half-life of a British garrison on the Gold Coast was less than 18 months. With this severe a disadvantage, I don't think there's anything the native Americans could have done, no matter how enlightened their chieftains.