I'm not sure about the frozen fondant question...but, maybe the template idea I used for the soccer balls would work for you.
I was determined to make good looking soccer balls. Well, I'm not a super fab piper. So, I made a template out of cardstock. I printed out soccer ball clip art the size of my cookie cutter. I then used an exacto knife to cut out the black shapes. I layed it over my cookies and outlined with an edible marker. I then went back and piped black over my edible marker lines & filled. After it set for 24 hours, I flooded the remaining shapes with white.
Maybe you could do the same with your zebra stripes. Except you may have to draw in your desired zebra pattern. Use your cutter to draw the initial shape. Draw in your stripes. Exacto knife them out & then lay over each cookie and trace where you need to pipe. They'll all the be the same pattern this way.
That would work for royal icing. Butttttt, I guess you could make a template for the black zebra stripes to cut from for fondant as well. Good Luck!