Chipmixer have Tor link, so they wouldn't know your real IP.
Converting Bitcoin to Monero is another option, but which exchanges you'll use? This will have concern about your privacy too. If you use centralized exchanges, they will store your data even worst ask your KYC. Bisq is fully decentralized and you can use Tor when set up the software.
My original BTC address is connected to me, and if they store the data, de mixed addressess will be connected also. Doesn`t matter if the ChipMixer works through TOR network.
In my first comment I wrote, that I want to use an exchange without KYC.