We had a similar problem. 3 days into our trip, my son's charging cord broke. We did have a hard time finding a lightening cord, but they are there. Pop only had charging kits for the older models and android....but we found a 5 cord at, of all places, the gift shop at Typhoon Lagoon. Another guest also told me there was a cell phone shop downtown, but we didn't need look as we found one elsewhere.
So if one gift shop doesn't have them....try another. Many of the CM's didn't have much knowledge about what they carry in phone accessories. You'd think with the new technology and people expected to have smart phones all day long.....the chances of replacements being needed would be pretty good.
regards