How to send my 2X coins to an exchange from a private BTC wallet I had during the fork? So, I have a private Bitcoin wallet for which I own the private key, it is not in an exchange. 

Despite the segwit2x fork was canceled, some people are still trading it and the segwit2x fork seems to still be user-activated. So it exists somewhere, isn't it?

I'd like to keep the BTC intact in my wallet and to send the 2x coins from the fork to an exchange. 

Which wallet or software could I use to send the 2x coins? I googled and nothing comes up except a website that suggests using eth wallets, which is a non-sense and seems scammy. 

Also, I would think of sending the 2x coins to another private wallet and then the BTC coins to another new wallet (so as to prevent replay attacks), and only then move my 2x coins to an exchange.
The 2x fork did not activate (there was a fatal bug in the code, perhaps more than one), so there is no 2x network on which to send coins.

On some exchanges, people are trading financial contracts issued by the exchange, which are related to the expected outcome of the 2x hard fork situation. This is different from an actual 2x coin (which does not exist).