Nice that you guys are planning an adventure. I’m sure it will be fun.
While most of the accounts mentioned in the group are not available to anyone residing in this part of the world, you are still on the accepted list. You can still get accounts from the likes of N26 and Transferwise during your trip.
Another option you could look into is using USD and Euro debit cards issued by our banks here. I know that Standard Bank has an international account but have not checked the details. Banks like Zenith and GTB will offer you this service same day.
Also look at online wallets like Perfect Money (I have been using them for years and am happy with them). You have countries like Georgia that you can walk into without any need for a visa and you can open a bank account same day. Open a few of these accounts and fund them (and your N26 or Transferwise) via perfect money. You also have the bonus of the bank debit cards that come with the new accounts.
Check to see if your local banks have branches in the locations you want to visit. With Zenith, First Bank, GTB and Standard Charted, I have lots of countries covered (London, New York etc) and they are linked to my account at home. Its easier to get our accounts with international offerings and services plus much cheaper to setup. Customer service is also way better.
Hope these help, enjoy…