I'd ship it in a one piece cheap plastic Walmart gun case taped shut then bubble wrapped inside a larger cardboard box.
You ship a gun in two pieces inside the same container you could be asking for trouble.
Actually the opposite is true. Shipping a gun assembled in one piece in a cheap plastic case is the best way of getting the stock cracked. Seen it numerous times. The case gets bent, and the stock is the first to give. Putting a 2x4 in the box with the case will prevent that.
I still takedown every gun I ship if possible and ensure they are separated well.
You have to put it in a stout bigger box with about 3 or 4 inches of clearance all the way around.
Guy shipped me a Fox 20 ga. on trade ....he shipped it in two pieces with each piece bubble wrapped...when it got here it had a massive dent in one barrel where the contents had shifted.
Needless to say it went back faster than it came.
A while back I shipped a 32" Winchester unsingle in one piece inside a cheap plastic gun box bubble wrapped inside a bigger box. I've shipped several shotguns in one piece without any problems....but I do have common sense when it comes to things like shipping.
