There are rechargeable hearing aid batteries that you may use as long as it is the right size and I have searched online and they have battery chargers too. Quite expensive though.  

Yes, you can use rechargeable batteries in your hearing aid. but why not try our rechargeable hearing aid instead? It comes with built-in lithium polymer rechargeable battery (just like your cell phone battery) and a free charger. No need to buy batteries. It can provide 20 hours of non-stop hearing within a simple charge of 3 hours.