AFAIK, there aren't any dropboxes at the resorts, (the FedEx app doesn't show any available in public areas either) but it's possible the front desk can take care of it for you. The Contemporary, since it has a convention center, has a business center that for sure will be able to take your FedEx package. Of course, they have to be open to do that, so normal business hours only.
One more option, if you have a car; there is a FedEx store across the road from Saratoga Springs (according to the FedEx site), and several other drop off locations in the area around Disney Springs. Check the site for all the locations.
Steve