Allow an extra day. My "toys bought Monday morning absolutely guaranteed for Tuesday delivery yes we know you're leaving Wednesday morning" between DS and the AK gift shop didn't make it. After much discussion, the gift shop manager agreed to ship everything to me for free. I received them about 10 days later. Not a terrible outcome but added unnecessary stress to our last hour at the resort. And disappointed the kids who chose those toys for the plane ride home.
Also, make sure you check your resort's gift shop hours if you're cutting it close. AK shop was closed Tuesday night when we returned to the resort. I was waiting at their door Wednesday morning to grab the toys and get to the airport.
We could have easily re-arranged our Monday to return to DS and pick up the toys ourselves if we'd known "next-day delivery" is open to interpretation.