I also believe it is hardly possible, especially if you want to stick to the mentioned box size.
The only way I can think of is glueing the cookies to a tray (with icing, not real glue), and ship them that way. But you would need a lot larger box for that, with probably much higher shipping costs.
Your solution with sending a picture as a suggestion is fine already, I don't really see a benefit in sending pre-arranged platters.