You can not ask any person to use a centralized exchange just to finish a deal and a transaction with you. If your trade partner does not use centralized exchange or don't want to trade with you and leak his privacy, your request will not be accepted by your trade partner.

P2P has KYC platforms and no KYC platforms and generally you can have tainted coins from them. If you don't want to have problems, you will have to move your bitcoin (received from your trade partners) to one or two more wallets of yours, before making a deposit to a centralized exchange. It takes more time, costs more on chain fee but if you want to take care of privacy you will have to pay some cost.