I know there are clear boxes. Alternately, put them in gallon-sized plastic bags. If the cards are put in the bags neatly and packed among clothes, they should stay tidy and shouldn't be damaged at all. If you're worried about what happens at your destination, flatten the card box and pack it separately.
When I was growing up, I had a card box that had basebally things printed on it. Storing cards in that would make it more obvious what the contents are.
So yeah, store it in something clear and/or make the box look more like a toy. Unidentified mass in a nondescript cardboard box would freak me out too.