Use an exchange wallet only for buying and selling Bitcoin. Do not store anything in an exchange. Even a hot wallet or a mobile phone wallet is better than an exchange. It least they won't ask you for an ID.
Also, I find that proxies will only increase the suspicion of cryptocurrency exchanges when you use their websites - as they can easily be identified by IP address.
Using exchanges is not only about buying and selling. It actually relates to other things like KYC (most exchanges nowadays are KYC mandatory), and even you only want to buy and sell your bitcoins through that exchanges, there is likely time you leave your bitcoin there, just longer or shorter time than people who plan to store and hold their bitcoins on exchanges.
It looks safer to store your bitcoin on a centralized exchange in a short time than a long time but when you do this, you don't have control on your bitcoin during that time, and there is risk of losing your coin.
Reminder: do not keep your money in online accounts.