What's the best legal way to "wash" your funds if you've been reusing the same public address for years?

I wasn't aware of the privacy issues associated with BTC address reuse and have been using the same public receiving address for years.

While setting up a new cold wallet with new seed phrase, what is the best way to transfer the BTC without publicly linking the two wallets?

I am considering sending the balance to a trusted CEX in multiple transfers, generating a new receiving address each time. Then sending the BTC in differing amounts to the new wallet, once again generating a new receiving address each time. In this sense, the CEX is acting like a "legal" mixer.

What method would you recommend for transferring from one cold wallet to another? If you break up the transfers in multiple transactions, what is the max amount that would not draw suspicion?

Note: This is not to evade taxes or launder money. Just regain my privacy and prevent against possible quantum computing attacks in the future