You haven't said which resort you're staying in? While I don't know if price or convenience is an issue for you, any of the Deluxe resorts and all of the DVC resorts have grocery stores. They can take an order for you and have it delivered in your room just moments before you arrive. If you have a room with a fridge, the CM's will even make sure your cold stuff stays cold, etc.
Granted, it is a bit pricier than going to Winn Dixie, but it sounds as if you are looking more to just have it done and over with. The Front Desk can arrange this for you as well as the merchandise shops.