Not quite.
Bill Nye is a guy with an engineering degree who has never really done anything with his technical training, and certainly knows very little about science.
Hawking is an important cosmologist with an over-inflated reputation among the general public that he does not have among his peers. His recent statements about Black Holes have been over-hyped in the popular press to promote controversy, but they are really quite mild and don't actually change any of the current theories about Black Holes much. The fact that Black Holes do not have an "exact" Schwarzschild Radius is not new; Hawking Radiation is essentially a manifestation of that fact, which has been known for at least 30 years.
Hawking is over-hyped because of a press fascination with the idea that there is a "smartest man in the world," a ridiculous idea on the face of it.
The most famous example of this myth was Einstein, a truly great physicist like Newton or Archimedes who only comes along every five hundred years or more. He was still not "the smartest man in the world," and by the time the press discovered him his great achievements were many years behind him. The fact that Hawking is disabled and has survived a horrible disease orders of magnitude longer than most adds to his mystique, but he's no Einstein, let alone the "smartest man in the world."
How can Hawking be a famous cosmetologist if he can’t use his hands? I’d hate to see his clients’ makeup.
Well said. Hawking just happened to become famous because he was in the right place at the right time. He’s smart, but not a genius. And these days I don’t think he’s nearly as sharp as he once was.
Einstein continues to amaze me.