The Swiss banks are the best if you don't mind AEOI.
AEOI is only between OECD members or they also share with other countries?
What offshore jurisdictions do swiss banks accept?
A country doesn't need to be an OECB member to participate in the AEOI program. There are maybe 20-30 countries in OECB but AEOI has thousands. Also a country doesn't need to sign the AEOI agreement to exchange information with other countries. They can always use other means: on request or spontaneously.
I don't think all countries have interest in sharing information.
I found this information:
https://thebanks.eu/articles/countries-which-will-not-automatically-exchange-account-informationAutomatically no, but upon request, (manually) they will unless the country is not in good relationship with the country. Don't forget that the AEOI program is born because of the United States and their Foreign Account Tax Compliance Act. Without this, It would probably never existed. And the US will surely use the pressure until more countries agree to sign the agreement. But for the sake of the diplomatic relationships, every country will share the information if it is asked.