With ChipMixer - cheap, fast, convenient, low risk, and secure. I can send coins to be mixed and leave them on ChipMixer for as long as I want, and access them at any time I choose. I can have a handy supply of mixed coins I can access at a moment's notice at any time. Additionally, thanks to ChipMixer's chip structure, I can only withdraw what I need, meaning I can usually avoid creating change which gives me even more privacy.

The only truly private altcoin is Monero, and the only truly private DEX to trade it on is Bisq. Swapping Bitcoin to Monero is a viable mixing technique, but you should then move the Monero around, wait as long as possible before swapping it back, swap it back in a different amount than you traded in the first place, and with a different third party. While this is entirely possible, it is slower, has higher fees, is far more cumbersome to do, and potentially less private if you mess up.

Also, if you are using a centralized service which is discriminating against some bitcoin because they claim they are "dirty", then that service is actively attacking and undermining bitcoin's fungibility as well as monitoring and censoring you, and you would do well to find a different service to use.