If you send btc to me directly and i have an unregisterd wallet, they will not know who i am unless my wallet gives out my ip. Use a good vpn like mullvad also.
Afaik, wallets do not store the information of your transactions (except probably it's not open source or is custodian). Transaction information are visible to the nodes which receive the broadcasted tx and they are the ones that can trace the IP related to it.
Using VPN services sounds secure, but it actually isn't especially for Bitcoin transactions. The protect you from someone looking in from the outside, but the VPN already has your details and most of them keep logs even if they say they do not.
For privacy;
• Run your full node, and
• Use TOR
Use mixers or exchange btc to someone "offline".
If you're going to do this, make sure you adhere to safety procedures or do not do it at all without sufficient means. There are a number of peer to peer networks which can connect buyers and sellers. Always do your own research.