How do international banks physically settle balances between each other?

The physical money is very, very little compared to the actual money that is settled.

In most cases, what the banks are doing is simply balancing the ledgers they have amongst them.

If there is physical cash to be moved, central banks sell this cash (printed notes) to commercial banks, and then commercial banks make physical flight arrangements to ship this money physically over to other countries (where in most cases, other commercial banks are buying this currency).

However, as I said, the actual movement of physical money is not used for settlement but facilitation where the physical currency is required.

If you want to learn how money is settled amongst banks, there is an answer I wrote that explains it in detail: Faisal Khan's answer to How does money transfer between banks and different countries work?