Where I'm from in the EU, many shops are happy to go card-only because the card fees (with the aforementioned EU regulation) are lower than the costs and crime

Where I'm from in the EU, many shops are happy to go card-only because the card fees (with the aforementioned EU regulation) are lower than the costs and crime risk of dealing with cash (which for supermarkets etc that handle a lot of it might mean paying a security company to show up with an armored truck, having to prepare change, staff pocketing some of it, etc) So if we're making customers pay the fees for their preferred payment method, is it also OK to charge cash customers a surcharge?