I imagine that some trusted source will establish microbanks for a limited number of American clientele, both for a fee and for business courtesy.
In either case, each microbank will have an equally discreet US equivalent, so if you say, deposit $100,000 in the US branch, an encrypted message tells their twin in the other country that you have a “line of credit”, of say, $90,000, no questions asked.
For maximum security, no data would be transmitted at all, using human couriers back and forth say once a week.
“for a limited number of American clientele”
I guess that leaves me out