If you use the resort delivery service you will be limited to only items stocked at the resort gift shop / general store. You'll also pay Disney prices (count on twice the normal grocery store price) and there's a $5 delivery charge.
A list of items can be found on the member web site. You can fax the list in advance for the quickest response.
If you have a car, I'd highly recommend setting aside 45 minutes to shop yourself. There's a Publix near the Premier Outlets, which is no more than 10 minutes away from OKW. And, while you're right there, stop in the Disney outlet store at Premier and you'll probably save a few bucks on souvenirs, too.