I think humanity will have a nuclear war and destroy itself.
But why do you assume a nuclear war would kill even the most reclusive native tribes?
My opinion is, folk still live close to Tchernobyl for example, where most of the fauna and flora, may I mention, thrives greatly. Nuclear impacts are certainly different than radioactive fallout, will kill tons of people, and may even have major ecologic impacts. Still I don't think we'd ever be able to create a wasteland as depicted in most postapocalyptic fiction.
I will make a nuclear bomb big enough to destroy the entire Earth.
Muahahahahahahahahahahahahaha!
I don't think there's enough Uranium on earth to do that. But good luck.