Do you know any exchange which accepts fiat money deposits without asking for KYC and AML procedures? I know only virwox but their fees are outrageous...
You tax data will be recorded even you use the direct account details or with the usage of your bank details while you paying up to the exchange wallet. I am not sure how do you looking to have the fund without kyc details.
KYC details will be asked in all the centralized wallets and exchanges so you need to go with the good best site if you wish by exchange.