Fees should not be your concern over safety, better to have your coins safe and incur a few extra dollars in fees, than trying to save fees and lose your assets when an exchange is hacked or when they decide to seize your coins for God knows why.
Of course, I'm talking about transferring to "safer", well known, long running CEXes, and not any run of the mill/"come-let-me-scam-you" CEX.
It does not matter the exchange it is, be it "well known" or "long running", keep your assets in your non custodial wallet and only send to an exchange when you are ready to sell.