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My husband is diabetic and we use Frio bags for his insulin, no need for a fridge. A friend took theirs on safari in Africa! Just soak bag in water (any water even a river) and place insulin inside. See their website: www.frio.co.uk.
On their website under cabin description they only mention the deluxe cabins and suites as having a mini bar., so I'm p[resuming they don't. That's not to say that the won't provide one (and a sharps bin) if you ask them. Cruise Lines are generally very co-operative when it comes to organising things that you need for medical reasons. Call or email them. Hopefully they will be able to assist you.
I was in the same situation both in January on Thomson Destiny & again in June on Thomson Spirit - no fridges in cabin, but staff on reception stored my insulin in their fridge until I required it. For daily use, cabin steward provided tub of ice twice a day to allow me to store syringe. Could not have been more helpful.
Insulin is quite safe to use for up to 6 weeks without being in a fridge.