-so, only a fraction of humanity will have access to changing themselves to be smarter and stronger.
Evolution was NEVER an equal possibility process.
This fraction of humanity will outcompete the rest - as in they/ their descendants will survive and the rest will dissappear, going the way of the dinosaurs -, as has happened many, many times in the history of life on Earth.
-even today, very few natural disasters can endanger a race of humanity as a whole - these are the type of disasters that endanger all of humanity (a gigantic asteroid, few others).
The regional disasters you mentioned don't even come close.
And that's just plain old "survival of the fittest" evolution like we've already had for millions of years. Significantly, we don't actually control which genetic modifications become the prevalent ones, or which populations in a competing genetic arms race actually win the battle for supremacy. Just because intelligent agency is involved doesn't change the underlying mechanism.
You seem to think that all competitors surviving and having a share of the future is a requirement of evolution.
It's a requirement of the type of evolution Stephen Hawking has in mind, where humans evolve based solely on what they NEED, not on the determinate and ruthless (and considerably slower) process of natural selection.