Great idea Ice Cream. I visited their factory and asked about converting an ice cream bike into a hot dog cart. The CEOs answer was "Sure, we can do any thing" And he meant it! Really am a big fan and devoted customer of theirs. They do some great work.
But to answer your question and more what I was thinking for the hot dog cart version, I am going with a Harbor freight 79cc rack mounted over the rear wheel. More then enough power, great engine and is ridiculous cheap. It's only draw back is it is big but rack mounted on a trike, don't matter much. Just my thunking and any of the suggestions will work for ya. Like the ewheel ideas. Could get a large solar panel. What are you gonna do for refrigeration?
Again, great idea and best of luck. Please post how biz goes. I'm really curious.