Depending on what you want to do on Castaway Cay, it can be a decent walk between things. So, you may want the wheel chair on the island. There are sidewalks for the main path between the shops, food, bathroom, and activities. But if you are planning on spending the day at Serenity Beach, the food, beverage, beach area and water are much closer together. There are no shops at Serenity Beach though.
DCL does have beach wheel chairs, if she needs/wants that instead of the long walk from the sidewalk across the family beach area.
The below link is taken from the Stern of the ship looking over the family beaches on Castaway Cay. The sidewalk path is back buy the buildings in the trees. The distance from the sidewalk to the water can be pretty long. The distance from one end to the other is long as well.
https://photos.app.goo.gl/iAkwtnBaxPk3J3Ug6