Get a (or a couple of) USPS Priority Shipping boxes. For a flat rate of I think $8.35 you can ship whatever will fit without 'stretching' the sides; weight doesn't matter.
The boxes come in two dimensions, but they may each hold about the same volume - I don't have the measurements handy.
When you pick up the box/es, ask the Postal Employee for shipping advice, i.e. how long it should take for the package to get from there to Disney. Ship it with a couple of extra days' cushion. Mark it clearly with your full name and arrival date. You can pay for one-way postage when you ship it; you can also print out at home your return shipping label if you'll be sending stuff home as well, and bring that and some tape to attach the label to the box.