Genovese, Casso would still be the same guy. He'd just be under Chin Gigante, if history were to turn out the same aside from his family affiliation.
A funny Casso story comes from the Five Families book. Gotti and Gravano are going to a Commission meeting with Amuso & Casso and the Chin. Knowing the heat between Chin & Gotti, they're in an underground garage. Casso looks around with this smirk on his face while they're going up to this meeting and Casso says "This would be a good place to do a hit". According to Gravano, he and Gotti almost shit themselves. It was the same meeting where Gotti bragged about making Junior and Chin says "sorry to hear that".
Was this the same meeting where Amuso got drunk and raised his voice at Gigante? *Story from the unreliable Phil Carlo book*