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.
Clean, taint, or mixing BTC we are still saying the same thing but have different beliefs about the meaning of the words and the origin of the vernacular.
Mixing or CoinJoining coins is a means to maintain or improve privacy, not to 'clean' your coins.
Yes, CoinJoining is a good means of improving BTC transaction privacy but I don't know if you're aware that a vulnerability was detected about its service years ago, and in other to prevent issue like this when privacy is the top priority is the reason why i suggested to use of 2-3 privacy service.
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.
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I'm not talking about the use of SPV wallet and when I said privacy wallet I am referring to Wasabi, Samourai, and Sparrow wallet