Try using cryptocurrency mixer or bitcoin mixer usually that's the service people use when they wanted to do an anonymous transaction or sending it to private address. Also, there is a wallet with a built-in Bitcoin mixer I think that was Wasabi wallet. I'm quite curious too what could be the other way to hide the transaction.
There's still a good mixer today that allows you to transact and remain anonymous but the effort of doing this is not easy for sure and you have to understand the system first before doing this. I didn't try to withdraw huge amount of money but seriously, of all the transactions that I have I don't think I can still transact on Private especially I'm more on P2P in Binance. This is a good question btw and maybe there's still a solution.