I am a diabetic, and have been on several cruises without problems. On NCL Norway, went to the Medical Office and stored my medicine in their fridge.
On Celebrity Summit for 14-nights, used the minibar fridge. On a Danube cruise, stored my medicine in the fridge in the bar. On NCL Mercury I had a minibar fridge brought to cabin. NCL even gave me a small plastic "Sharp Safe" to store my used needles.
Just talk to the cruise line before hand (several days ahead) and they will take care of your needs.
Get a note from your doctor listing your meds. Wear a MediAlert bracelet or necklace. Carry a card in your wallet or purse listing your meds.
Enjoy your cruise.