If you are willing to trade just crypto vs crypto then many exchanges don't require verification. Your ID check is a must if you want to exit to fiat
This.
Most exchanges only require a email for most to be able to deposit crypto and than trade crypto to crypto. They will make you send a ID and a photo usually when you are requesting payouts over 1-2 btc per 24 hours. Although note of advice if you are going to be only having a email for a exchange I would definitely have 2factor auth for your accounts. That way it is pretty much impossible for your account to get hacked.