The specifications should include the G-force and temperature limits
specified by the tape manufacturer. In the context of a DR test you might
want more stringent temperature limits to avoid waiting for cold tapes to
warm up to room temperature.

I have seen computer equipment shipped with special labels designed to
change color if the shipment was subject to out of specification
conditions. You might want similar labels for your tape shipments.

Depending on your concerns about confidentiality, you might want
tamper-evident seals for tape containers.

If you are subject to specific legal requirements for data protection, the
contract should include an explicit committment from the vendor to conform
to those requirements. For example, my employer is a hospital, and all
contracts that involve entrusting clinical or billing information to
vendors include provisions stating that the vendor will comply with HIPPA
requirements.

The carrier should have a bonding contract that would compensate you for
lost or damaged tapes.

We use an outside vendor to transport and store offsite tapes. Our auditors
have been getting very fussy about having an auditable documentation trail
for each change of physical custody of tapes.