Hi Caroline,
When you say US hair straighteners, I'm not sure whether you mean a chemical relaxer or an electric device that we might call a flat iron. While these items are not sold everywhere in the parks, it is possible to get both types of hair straighteners in the salons located at Walt Disney World. The selection will not be large, but the salons do have a very small selection of beauty supplies for sale.
I've personally used the Ivy Trellis Salon at the Grand Floridian many times and have seen small flat irons for sale on the shelves near the register. There are also salons at the Beach Club, Saratoga Springs Resort and the Dolphin hotel. The
Mandara Spa at the Dolphin would likely have the largest selection of beauty supplies and the gift shops at the Swan and Dolphin will likely carry flat irons for hair straightening.
Additionally, any of the salons would do a great job of straightening your hair for you.
Good luck with your planning. Please let us know if you have additional questions.