+1Hell, nuking him would fit right into Lovecraft's mythos - that kind of truly terrifying application of physics, that kind of incredible, insane power, is the very stuff that all the weird things make use of themselves. Nuking Cthulhu, using nukes at all, is just another step down the path towards being just like the Old Ones.
Although, if you kill Cthulhu, what will the younger races do? From what I understand, there are races that are afraid of mucking around with things on Earth because there is a great old one hanging around. Kill him off and then the younger races might come out en masse.
Edit: Might also think about what the Deep Ones will do when their god is dead. Mass suicide (lots of weird fish bodies floating up all over the coast). Mass murder. Splintering factions. Worshiping other Old Ones and trying to bring them here.