Or they set up a multisig wallet, each creating one keypair directly on approved (tamper resistant) hardware wallet models, transfer it to the multisig wallet, and now control of the collection of multisig wallets means you control the token.

So now you trade it by trading the set of hardware wallets. Validated by each original participant including results from an audit of the key generation procedure with the hardware wallet.

No trace on the blockchain, and the trust model is more robust than simply taking the word for it as one of them share the private key claiming they did not keep their own copy.