I've taken insulin to India and back, not used the hotel fridge, just resoaked the Frio every 3-ish days, bunged the unused stuff back in the fridge at home when we retured, and NP. Also the Carribean, Maldives, Australia ........ and quite a bit of Europe, Stratford upon Avon, France motorbike touring/tent camping ....
I shouldn't worry too much if I was you, just make sure you have some fresh to come home to though in case. Normally on return, I've lobbed the 'in use' cartridges that have been to the beach, up mountains etc and put one in out the Frio and just used them in favour of the continually fridged ones. I can honestly say I've never had a problem.
Incidentally FWIW I've usually found the back of the wardrobe to be the darkest coolest place in unairconditioned rooms, because they are normally situated well away from windows and the sun. Somewhere we went where there was a safety deposit box in every room and you got the key for a few pence, that was cooler than the wardrobe being metal and embedded in an inside wall, so the Frio sat on top of the passports etc for a fortnight. The passports were in leather wallets which went a bit mouldy from the damp and we had to sling em! LOL