It seems like somebody will periodically have to pop off EMPs to ensure that every transaction evermore doesn’t go completely digital and forever trackable.
One thing you can be sure of. Those in the financial system have ensured that EMP's will not affect the equipment used to store completely digital and forever trackable information.
Besides that, were there to be large enough EMP's to critically wound our financial system, we'd all be dead in a week or two anyway.