That’s highly unlikely to happen. We may never have the technology to detect Hawking radiation from a stellar-mass black hole, even from close range, which means that it would have to be a smaller black hole that we find somehow, or one that we make ourselves. In both cases, were that remotely likely, it probably would have already been done. I should also note that Nobel prizes are never given posthumously, so if you don’t live to get one, you don’t get one (though if someone ever does observe Hawking radiation, the person who made the observation might get the Prize).
I’m not even sure how relevant Nobel prizes are to this discussion. First of all, they’re biased against theoretical work (Nobel wanted to reward work with practical implications to helping humanity), and some fields of science don’t have a Nobel prize at all. And the work for which a person is most famous is often not the work for which the Nobel is awarded. Einstein’s, for instance, was not for either theory of relativity, but for his work on the photoelectric effect, and Michelson’s was not for his disproof of the ether, but for his work in establishing standards of measurement.