What is the safest way to withdrawal bitcoin from cold wallet into cash

Im relatively new to this scene so please forgive me. But i cannot find anything online explaining this to me.

I understand the concept of storing bitcoin in a cold wallet for the purpose of security and not storing on the exchange. But when I want to withdrawal my bitcoin, wouldn't i have to send the bitcoin from my cold wallet to an exchange? Does this not mean that all my bitcoin is now back on the exchange under a private key i do not own? Yes i can withdrawal into fiat and then cash but could the exchange refuse as i've heard in the past? or worse yet, have my bitcoin compromised during the time my bitcoin is on the platform.

maybe im overthinking it but i thought having a cold wallet was to not have all my valuable bitcoin on the exchange but i have to send it back to the exchange anyway to withdrawal?

All support is welcome thank you!