The only scam I've run into is the hearing impaired, want 400 cupcakes picked up by courier one. I've gotten that a lot, but just delete and move on with my life.
I only accept cash or credit cards for final payment. I started selling a little less than a year ago and within the last few months tipped the point where I'm selling more to strangers and less to family/friends so I've become a bit more cautious about forms of payment and a bit more diligent about requiring deposits. I think to be competitive, credit cards need to be accepted. Cash only isn't practical, especially once you start selling orders for several hundred dollars a piece. And for deposit purposes, Paypal is fantastic (minus the fees, of course!). I tend to do almost all of my communication via email so it's super easy to send a Paypal invoice and collect deposits. I will accept checks, but only for deposits so there's plenty of time for it to clear. And I let the customer know that until the check clears their date is not reserved. Most choose the Paypal option.
And I agree that the credit card fees stink, but I think it's just another cost of business that needs to be worked in. I haven't been scammed accepting one yet, so fingers crossed. And I tend to agree with others that a custom cake would not be the likely target of someone with a stolen card. Usually there's several weeks of back and forth communication with the customer, it's not an impulse buy. And if you require a deposit you would hopefully find out about the fraud well in advance of any actual baking or delivering of the final product.