By identity info I'm guessing you mean bank accounts, driver's license/passport, even phone numbers?  You don't need any of that on any exchange UNLESS you are doing fiat.  I personally use bittrex and poloniex for my crypto-to-crypto exchange needs.  Bittrex doesn't even care if you use a temporary email (yopmail) to set up an account if you don't even want to use your main email.