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's 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.
You're right. Not suitable for using the term "clean your BTC" because the function of mixing is to increase privacy by obscuring personal data or keeping secrets when making transactions.
I am sure he has a positive purpose behind the pronunciation of the word "Clean your BTC" and does not intend to say dirty bitcoin that needs to be cleaned using external services because there are two types of mixer services, the first type is centralized and the second type decentralized.