I don't know about this particular case. Seems to me simple 5" by 8" padded envelope would work pretty well. But I have heard that some companies have found that package delivery services have a better record of reliable tracking, safely shipping and not damaging boxed that are a good bit larger than they may need to be. Smaller boxes have a greater tendency to 'fall through the cracks'. Sometimes literally.

On the positive side it got there. Something of a novelty I think sometimes. And they gave the clip 'room to breath'. So it arrived relaxed and ready to go.