It depends on the quantity of crypto currency the OP wants to trade. Binance in particular would require KYC for some certain amount of crypto currency traded in their platform and if the OP is to trade a large quantity then he will  definitely need to do KYC to increase his limits of withdrawals and deposits. But if you read his statement carefully you will  see that the OP wants a non custodial wallet that doesn't require him to be Kyced or uploaded any of his identity or any other details. What he needs is a decentralized exchange and I believe some persons might have dropped some for him, so it is left for him to research on them and choose the one that suits his interest.