Answer first: for a lyophilised solid the cold chain matters far less than people believe, and for a solution it matters far more than they act as though it does.
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.
Phase-change pack hold time is a function of mass, latent heat and insulation, and published figures for small parcels are on the order of one to two days.
The domestic leg is the part you control. Refrigerate it promptly.
edited 7 Feb 2025 by tobias_maartens — fixed an arithmetic slip in the third paragraph