There is huge chance for you to clean your BTC through the strategy you posted but if you must do the process make sure the exchange is DEX,
I don't like the term "clean your BTC" because there is no clean, dirty or tainted BTC, all BTC are the same and this terms are created by centralized anti-BTC institutions to attack the network. Mixing or CoinJoining coins is a means to maintain or improve privacy, not to 'clean' your coins.
However, I will advise you also make use a privacy wallet just in case there's a lagging which could expose your privacy.
Privacy wallet for BTC? To achieve privacy you have to run your own full node and verify everything locally. Let's say you use an spv wallet like Electrum without connecting to your own Electrum server over tor but you use a third party server, your privacy is exposed to the server you connect to.