They do have wheelchairs that are designed for use in the water (by request, it's not sitting out).
I don't know if they will let you, but if they do, you don't want to push your own wheelchair into the water past the axels - the water removes the grease from the wheels. That makes the wheels squeek (found out by experience).
Also, be aware that even though it is a zero entry pool, it's only about 3 feet deep at the deepest point.