Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
Not sure how detailed your screens are going to be or if this would even be any safer but you could use vinyl. Weed the design and then stick the vinyl to the screen and print away. I cant imagine a design on a cake coming out really crisp anyway. Strange request for sure.
eff the emulsion, would you eat anything that had been through a screen print shop?
back in the day when I ate junk, I used to send my pop tarts down the dryer. 2 trips through and done, son. I printed milk chocolate on rice crispy treats once...what's food grade?