It's likely they will ask you KYC verification and write all transaction details. If government decide to track you, you'll be tracked easily.
Those exchanges use KYC only when using important amount.
Wasabi is Bitcoin wallet with built-in CoinJoin, not mixer.
Coinjoin is putting different amounts of BTC from different persons in one or several transaction and then getting several outputs with the same amount so that It is difficult to know to whom the outputs are.
But if your name is tied to a transaction and another transaction in the coinjoin process is tied to criminal activities, The authority will make no distinction even if you are not involve.
Mixer way of working are not so different from coinjoin. You put some BTC with other people's BTC, then several transaction are done. Then you recover your BTC on different addresses.
I have heard that mixers are now illegal in the US. Some mixer have been shut down and mixer owners condemned.
are you from chipmixer (because you promote it)? is it reliable?
is flyp.me reliable?