If the chronometer does not have the external arresting device on the bottom of the tub, it must be secured manually by removing the movement from the tub, securing the balance from moving and putting it back in the tub.
If one is careful, the tub with the movement in it can be placed inside the box with adequate padding. However, it should be removed from the gimbals. The reason is that the two screws that hold the tub in the gimbals will get movement shocks no matter how well packed the interior is. The mass of the tub will cause them to come loose and bang about.
You can flip the tub upside down in the gimbals and take a picture of the bottom, we can tell you whether or not it has a locking device. It shows as a second opening on the bottom that accepts a hex shaft to move the device inside the tub (if it is there).
If it were mine, I would only ship it first class registered mail to ensure that no one will throw it across a room. Each USPS employee who handles the package must first sign for it in the permanent log.