Yes, if you take credit cards, you'll have loads of issues. But for example supporting the eurozone (most of the EU) is both easier and better accomplished by only taking SEPA push transfers. While there is fraud risk, it's significantly less and shouldn't cost you as the processor. Worst case, I think, it'd be the cents you have to pay to send the money back.

And regarding the issue with being a trust: sure that's a thing, but contract terms should be able to fix the problem by making you send it back (minus nominal fees?) if the designated recipient's registered IBAN refuses your payout. And just don't offer to collect money for anyone who didn't register.