The honest answer is that the cold pack is doing much less than people think and that shipping lyophilised is what actually protects the material.
Anything shipped in solution is a different risk category, because hydrolysis and deamidation proceed in the aqueous phase and are strongly temperature-dependent.
Once the parcel arrives, the domestic leg is the controllable part: get it into the refrigerator promptly rather than leaving it in a warm hallway for a day.
Single-use temperature loggers are standard practice in supply chains where temperature genuinely matters and are inexpensive at parcel scale.
Reconstituted material has a genuine cold-chain requirement and it starts the moment water is added.
The domestic leg is the part you control. Refrigerate it promptly.
edited 4 Aug 2024 by w_okoye — reworded for clarity after a comment