Maybe you are looking for a Non-CRS country that does not make any kind of banking reporting. As far as I know there are 12 and they are Ukraine, Serbia, Philippines, Paraguay, Montenegro, Macedonia, Kazakhstan, Guatemala, Georgia, Dominican Republic, Cambodia and Armenia.
Check list of banks, emi's etc in another forum written by Darkster and others and select a bank or emi from one of these countries and do a firm research before joining.
More than 100 countries have signed up the Common Reporting Standard or CRS, which also include most offshore and tax heaven. The days of Banking privacy is almost gone. So it seem like there is only these 12 that are still available for our use. Eh! See the list:
CRS by jurisdiction - Organisation for Economic Co-operation and Development