You can use a peer to peer exchange like bisq to maintain your anonymity. I know Ethereum is accepted on bisq, but not certain on the other altcoins.
Using a bridge between to obfuscate the trail of transaction can also help, this involves using a coin mixing service like chipmixer before sending to the decentralized exchange. This way, anyone monitoring the transaction would not know the source of the bitcoins which were inputs in it and cannot link it to an identity.
Do you have any idea if centralized exchanges (specially Binance) usually freeze or limit accounts of their clients in the case they make deposits with mixed satoshis?
I ask because I have got some mixed ones I got as reward for some review I made for a mixing service, but I am not sure if send them to Binance or any other centralized service.