The FICA stuff is adhered to in most overseas countries. Switzerland is an exception, but you must still be there and have a substantial initial deposit. Beware there is negative interest there. I have had an acc with Bank Leu since the 1970's but keep a very small balance, ChF50,- to avoid negative interest
You are also supposed to notify SARS about foreign bank accounts
Some banks in the Cayman Islands are more relaxed about proofs, etc but again, will not look at you without $10000 to deposit