I think you would help it. The nuclear weapon is not going to make all the water disappear (except technically the water very close to it). It would heat the water in the hurricane allowing it to rise further. Then the water would precipitate starting a powerful cycle. While I can imagine that a nuclear weapon could disintegrate 'part' of an eyewall, it does nothing to remove the energy source or the moisture, so a new eyewall would rapidly form. The best attack might be if you dropped it significantly above the hurricane to one side to try to disrupt the outflow patterns (since you would be attacking the dryer air). But while nuclear weapons are impressive, I don't think they stack up anywhere near the power of a hurricane. A Hiroshima type blast would hardly be noticed. A 10 MT blast might cause more disruption, and I'd have to check the overpressure ratings for it, but I doubt that it would be effective more than perhaps 100 square miles (of something that is tens of thousands of square miles). I think the best response would be nothing more than causing an eyewall regeneration cycle. Of course, I'm not a meteorologist and I've never used a nuclear weapon (though I do have a very nice .40 cal handgun). I just have a strong knowledge of evaporation, boiling, and condensation from working on nuclear reactors.
The radioactive fallout would be blown far and wide.
Yeah, apart from that little radiation issue, I was thinking something along the lines that it may actually intensify the hurricane.
I have never used a nuclear device either, that's why I'm a bit unsure of the effects.