OK, I will go through the KYC procedure, and what will happen to my anonymity? All data about the user will be known, and anonymity is something that is very appreciated.
Among the exchanges that EDC is available in them, Yobit doesn't require you to pass KYC. If you want to remain anonymous and you don't want KYC, you can use Yobit.
If I am not wrong, On Coinbene withdrawing coins and tokens up to a certain value doesn't need to pass KYC. Coinbene might be a good option for you too.