Thinking back on my experience over the years:
1) The year I got an Owner's Locker, I shipped a big box to Boardwalk Villas. I stopped at Bell Services. The Bell Services guy grabbed a cart and walked over to the BoardWalk Convention Center business office with me. The Business Center person put the box on the cart, and the Bell Services guy walked to my room with me.
2) Last year I had a small package shipped to BoardWalk Villas. I could have carried it, but I was not going to be in the hotel during the hours that the Convention Center's business office was open. I went to the front desk one evening after the business office had closed, and asked them to get the package for me. I waited in the lobby and they brought it out to me.
3) When I had a package shipped to Beach Club, I walked over the Yacht Club/Beach Club convention center. The cast member in the business office told me that another cast member who normally works in the business office was out delivering a package to a guest's room. My room was not ready yet, so I took the package to Bell Services and left it there. When my room was ready, I called down and had Bell Services bring the package up with my luggage.
4) At Animal Kingdom Lodge - Jambo House, there is no convention center. The package was delivered to the front desk. I called down to Bell Services and asked to have it brought up to my room. Bell Services said they were not allowed to do that. I had to go down to the front desk, wait in line, and ask them to bring it up to my room. A cast member who was not affiliated with Bell Services brought it up to my room.
A note about shipping: it's not cheap. You can price it out on the FedEx and UPS website.