Public reputation? Certainly not. How many other cosmologist or quantum physicist can the average person, or even I, name? Approximately zero.
Scientific reputation? I understand that he has produced some pretty significant theoretical advances, but maybe even in that circle his disability has enhanced his fame and reputation.
Ouch!...Long ago, did PCism rear its ugly head...and Who could do that Math?
Hawking was already good and hot in physics before he became disabled. He would probably be even more famous because his illness has slowed him down, no two ways about it.
It took SH for us to find black holes. But his theory was only that, theory.
Since we cannot enter a black hole "WE" cannot get information. It is not that SH is wrong. It is just like all science, more information, better technology, allows for more details.
SH would be where he is wheelchair or no, he is one who uses his brain, he thinks.
Newton did not invent the telescope. It was a toy and he stole the idea and sold it to the Navy as his own. but he did make better lenses.
What makes SH better is the fact that there is math that has yet to be considered. It took a girl just a year or so ago to solve a math problem that mathmeticians could not do for centuries.
The difference is that SH will say he was wrong flat out, other scientists never admit that, they just say they there thoery "evolved"
After trying "all" the computer models they could think of about the formation of planets they all worked on the planets except Uranus and Neptune, for some reason the Gas Giants do not allow themsleves to be figured out yet.
Once they "solve" that little problem it may completely change the way in which the universe sould have been formed.
Only time and technology will tell.