I never heard that there is a safe exchange site with no fee. So, I advise you to trade in some trusted exchange sites with a low fee like Cryptopia, Bittrex, and Binance.

I recommend you choose Binance because they had 50% trading fee discount for the 1st year.

You can check this discount from their support area here Binance Launches New Tiered Trading Fee Discount Program and Adjusts BNB Discount Rate