They don't accept CC, but I'm pretty sure they accept Disney Dollars.
You can check at Guest Relations when you enter Epcot, and if they don't, they can cash you Disney Dollars for regular money... and then at the end of you day just stop back buy and exchange for Disney Dollars again.
According to a Disney web site:
Q. Is there anything I cannot purchase with Disney Dollars?
A. No, Disney Dollars are treated the same as cash, however, some 3rdparty vendor locations do not accept Disney Dollars.
Some of the restaurants providing the FWF Booth food are 3rd party vendors (such as Mitsukoshi in Japan) so you might have to skip them or pay with regular cash.
This is worst case scenerio though, I am almost positive they accept Disney Dollars at the booths - I just have never done it