Costumers don't pay fees for having a CC. They pay fees because CCs exist, regardless of whether they have one or not. Which means using Dwolla or a CC is irrelevant in that regard.
Many PoS merchants also now charge surcharges for using cards. (which I admit for a merchant only makes financial sense if you underreport cash on your taxes--otherwise it seems the costs of handling cash coupled with lack of reporting is drastically more than the interchange).