I got a special tree that exploded completely in the box. it was taped, padded, and all, I almost cried when I saw the scene.... there was not one root left on the cutting, so I started the process all over, but only let it rest a couple of nights and planted back in same pot it came. I put inside of a grocery plastic bag and tied a knot on top. Put in my window and today I see a new leaf sprouting, which tells me new roots have emerged. It is my experience, that you should not send the dirt that is not really necessary.
I would get a aluminum foil and open the cup gently, shake off the loose dirt that is not anchoring roots, the remainder, you spray it a bit and make another aluminum foil clump ball (sort like the airlayers we saw in videos) make it tight, take the cutting and the bottom covered in foil to another cardboard. prefolding in 3 or 4 carboards works great. After I sent you (my first shipping) I have learned and the people I sent received and have no complaints, except for one Adriatic that exploded on the way that took some 10 days.. I think they made it into a football or something, because it was taped to the container.
I am sure you will figure it out..less soil is less cost in shipping for sure.
if you get some of the post office flat rate, and manage to pack to fit in those, you are better with costs. because of the dirt... I have fitted plants with soil into those flat small containers.. very cramped, but enough to shove in a few peanuts or shread paper to really pack it.
my package from a nursery also exploded, they taped the dirt but the package was too loose inside of a much larger box.