Any exchange is more than capable of looking back a few transactions to see where the coins have come from. A far better option is to stop using centralized exchanges which attack the very essence of bitcoin by treating it as non-fungible, and will spy on you and censor you if they don't like what they find.

There are now plenty of decentralized exchanges, marketplaces, merchants, services, and so forth, out there which do not spy on you and do not promote the provable nonsense that some coins are "tainted". Use them instead, and stop worrying about whether some faceless third party thinks your coins are naughty.