After buying crypto with fiat on a KYC exchange, instead of just moving the crypto to a wallet, I understand that I should get more anonymity from tracking by putting the coin through coinjoin or whirlpool. But it would actually be more economical for me to buy LTC on the exchange and send it to an online exchange like Changelly where I could exchange the LTC for BTC and then send it on to my wallet. (More economical because my exchange charges much more to withdraw BTC than for LTC.) But I wonder if the swap may give anonymity to the BTC. If that is so, then I wouldn't have to go through the coinjoin process, which seems complicated to me. Does anyone know if non "know your customer" exchanges provide as good anonymity to crypto as coinjoins do?
Ideally you should never use KYC exchanges with or without coinjoin. The record with the exchange and third parties that manage KYC stays forever about your real identity and bitcoin transactions.
Swaps done using services like changelly do not provide anonymity. The service has all the links for your transactions and in some cases it could be tracked with chain analysis.
Quoting from https://changelly.com/aml-kyc :
We obtain and hold required and accurate originator information and required beneficiary information on virtual asset transfers and make it available to appropriate authorities on official request
Coinjoin is a transaction between some users that try to break the history of their UTXOs. Outputs in a coinjoin transaction look similar and its difficult to associate them with any inputs.