I am not aware of such "crypto exchangers" that you mean. You can say it by the name though, for references.
What system is used in Ireland for transferring EURO between private card holders during P2P process?
I don't know specifically how banking works over there. But for an example, decentralized exchanges like Bisq offer various methods of payment, especially on EURO.
You can see the payment method with its limitation that are available on Bisq here:
https://bisq.wiki/Payment_methods. The available method may vary since it depends on the buyer itself.