The transaction key is for proving that the transaction has been made and that it originated from you. It's specifically made for such occasions of dispute etc. It doesn't hurt your privacy or reveal anything else other than that transaction. From Monero.How:
In Monero, a payment proof does not reveal your wallet balance or full transaction history. Instead, it allows a specific verifier to confirm that a transaction matching certain parameters exists and was created by the sender.
More details are in the linked article.
Though it is generally advised to make an entirely seperate wallet for CEX interaction.
Whats the CEX that's giving you trouble ? So that we can be wary of them if the issue persists.