Can I use a rechargeable hearing aid battery in my hearing aids or do I have to have hearing aids that are set up for rechargeable batteries.

If your hearing aids use batteries, and those batteries are available as rechargeable, sure. But it's much simpler just getting rechargeable hearing aids. My Oticons are good for the whole day; they spend the night in smart charger (which has a battery good for several charges if it's not itself plugged in to stay charged).

Rechargeable hearing aids are available, not sure though about the rechargeable batteries for hearing aids.