The Port of San Diego and the San Diego airport are very close, that is, they are about 15 minutes apart. You will have time measured in hours between disembarking and reaching the airport. A taxi would be the fastest and probably cost effective in comparison to a private shuttle. But this is one issue you should not worry about at all.
You should plan on arriving in San Diego the day before your cruise or even two days (and two days in San Diego is a wonderful travel experience) if the weather is iffy at the time of your cruise.
Hope that this helps.