>...then* 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.)
SWIFT abides by international law and local laws. Including those against processing money transfer requests for terrorist organizations like A/I.