A single smallpox laden explorer would have started a plague in the Americas and a single native American would likely have died of one of the many plagues in Europe that Europeans had grown up with (and still often died from).
The problem of safety is not always placed on the explorer, sometimes the explorer is the danger to his environment.
The point is that entire classes of extremely common diseases in Europe basically didn't exist in all or most of the Americas, and many of those diseases spread very easily once even a handful of people had carried them across the ocean.
A single smallpox laden explorer would have started a plague in the Americas and a single native American would likely have died of one of the many plagues in Europe that Europeans had grown up with (and still often died from).
The problem of safety is not always placed on the explorer, sometimes the explorer is the danger to his environment.