Don't use localbitcoins as suggested above. It might be peer to peer, but it is centralized and will absolutely required KYC and other information from you.

There is no centralized exchange in existence which is entirely safe, and even ones which offer non-KYC accounts such as KuCoin can and frequently do lock accounts and confiscate coins while they demand KYC. If you aren't comfortable submitting KYC, then you need to avoid all centralized exchanges.