Welcome aboard, Lex -
Just a few more days and you'll be setting sail with Captain Mickey for the very first time! You are in for such an amazing experience on the Disney Cruise, and I can already picture your son's delighted face when he starts exploring all that the Oceaneer Club offers. Be warned, that he might want to spend more time at the Youth Clubs than with you for the duration of the cruise. :-)
Since you are having dinner at the 2nd seating around 8:15pm, you will actually be watching the 1st show schedule at the theater at around 6pm. My family and I actually prefer this schedule, since my kids get to enjoy the shows first -- and then we all have a leisurely dinner afterwards. If you think your son will get hungry earlier, you can always pick up a small snack to hold him over at the quick service counters by the pool deck. There have been a few times, when I've ordered some chicken noodle soup from the complimentary 24-hour room service too - just allow about 30 minutes or so for the food to be delivered to your stateroom.
if your son still has energy after dinner, then he can always head back to the Youth Clubs to play... otherwise, he might be calling it a night and waking up really early the following morning to enjoy another fun-filled day. But at least, all of you will get a chance to watch the awesome Broadway-style shows.
Pirate Night will be an after dinner deck party though -- hopefully, if he sees all the excitement going around him that evening, it will keep him awake and he'll have the energy to come up to the deck to enjoy this signature 'can't miss' event... swashbuckling fun for the whole family!
Hope this helps. Please let us know if you need any additional planning help for your upcoming vacation.
Bon voyage!
~ Dolly