If Italy doesn't shut down their services, the Italy itself will be shut out of SWIFT.
SWIFT is headquartered in Belgium. Only 2 banks out of the total 24 on the board of directors is US banks. Unless there's a hostile takeover of the SWIFT organisation by the US, I think this is a bit of a stretch. (Plot-twist: Italy is on the board of directors.)
A US sanction is neither a local (to all of SWIFT) or international law. The question still stands.
US laws and sentences does not apply beyond US borders unless differently agreed.
Because of a decision from the USA administration? ?!