Retaining control of the contents of your wallet should be more important to you than a potential quick profit from getting to dump the losing chain.

If your bitcoin is on an exchange, it's not "your" bitcoin any more, regardless of what the exchange may say or promise. They may cut and run, they may Gox it up, and you've got no control since you don't have the private keys to "your" bitcoin. It's only yours if you have those keys and nobody else does. Nobody knows what's going to happen when Segwit2X goes down, and nobody can predict how the exchanges will respond. Stay safe, and stay in control.