I would bring the kind of wrapping paper that comes folded, if packing it is an issue. Or tissue paper and a gift bag. They also don't sell greeting or birthday cards in the parks, so bring those. And be aware that you may not be able to bring a wrapped gift through the bag check. If it's small and they don't see it in your bag, it may pass. But my friend was stopped with a larger box, about 14 inches. She had to partially unwrap it to get it into the park.