I would pack at least two per day, making sure that I got Space Saver bags(or something similar) to put the swim diapers in. If you have enough suitcase room, pack *more* per day & then at the end of the trip fill the empty space with souvenirs

lol.
Just a thought...Will you be renting a car, perhaps taking a towncar? Then you can buy some swim diapers during your shopping stop on the way to your resort. If you're taking Magic Express, maybe take a taxi from your resort to one of the reasonably priced/nearby supermarkets or a WalMart. You can buy all sorts of goodies & necessities(including swim diapers) for your WDW time. I've never used one of the shopping services, but many DIS'ers use wegoshop(At least I *think* that's the name...) or similar services.
There's always the resort sundries shop, but (ack) those prices...
Have a wonderful time! (By the way, your son is very cute! I'm sure you'll have so much fun.)
agnes!