Another thing you need to be conscious of is whether your mixed coins have the telltale signs of being mixed. Though a third party service won't know the origin of your coins, if they can clearly tell they have come from a mixed transaction then they might get arsey. Binance Singapore have been giving Wasabi coinjoined coins the boot because of that.
Some people think that simply using mixer service will help them totally hide with perfect privacy and ignore steps that they should do. From the Guide and FAQ of Wasabi, they emphasize importance of steps before and after mixing. They tend to forget the steps after mixing and recombine mixed coins.
https://www.reddit.com/r/WasabiWallet/comments/avxbjy/combining_mixed_coins_privacy_megathread/