Whatever method you choose to ship will NOT be careful with your package. You need to take protection measures.
I have shipped in cups successfully. You just need to pack well so the soil stays put, and the leaves are protected. I cover the soil with seran, top with peanuts and more seran. I tip to the side, roll in corrugated cardboard, and tape ends and the entire thing so it gets no punctures.
I have received many larger plants that were packed in good cardboard boxes with dowels protecting the leafy branches, and measures taken to keep the soil in the pot.
It's much easier to wait for dormancy, rinse the dirt off the roots, and keep them damp on their trip. Much easier and much less costly!
Suzi