VISA is widely accepted but they would still need some cash if they are planning on buying any trinkets. They are going to need cash to buy drinks etc...
As far as linking a different card to each person, I have tried that, without success. I don't think the computer system is set up to allow it. They always look at me like I grew horns when I ask them to set it up that way. You can dis-allow them to sign for stuff but that doesn't solve the problem. Maybe someone else has had better luck in this area and gave give you some advice?
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007