Would you be able to elaborate on what you mean by "one wall handball?" If it's the sport I'm thinking of, it's played outside NYC as well.

Coming from Massachusetts, I played two different games called hand ball as a kid that involved one wall. One was also known as "wall ball" or "butts up" and the ball was generally thrown, while the other was roughly similar to squash or raquetball, but with hands.

Are you talking about a different sport than either of those?