A hurricane takes around ten seconds to transfer as much energy as a one megaton nuclear bomb.
Yes, but a nuclear bomb releases all that energy in a fraction of a second, generating very high temperatures. In other words, while it may not be a great method to stop hurricanes, I think it might work to disrupt and disorganize it enough that it breaks apart.
And it is driven by rising (warm, damp) air in the eye, so adding more heat to the eye in the form of a nuke would probably cause the system to get a tiny bit more powerful.
Presumably it would be detonated at the top of the hurricane then, where all the heat flows to. That would also help push almost all fallout to the stratosphere, where it would be distributed evenly and slowly (taking care of more radioactive but shorter halflife isotopes) across the Earth.