I see that Perche's arguments convinced you: good, because that saved me from writing the same answer. Naples in January is great, also because it's not hot. An occasional shower, but that also adds to its charm. Go for it!

PS And if it's not raining, go see the fish market at Pozzuoli and take a stroll in the crater of the Solfatara volcano. Then you'll have an experience that your wife hasn't had!