Low carb cruiser checkin' in here! A few months ago we did a 14 day TransAtlantic, and I was a bit concerned about staying on plan for the duration, having disembarked from several other cruises with more "baggage" than I started with. I needn't have worried: it was low carb heaven!
Sure, you could pack up your MiMs and ask to have them stored, or store them in your stateroom fridge. If the fridge isn't cold enough, consider packing a small, soft-sided cooler -- ice is easy to come by. In that case you might want to pack ziploc bags too.
But why bring something you can have at home when there's bacon, sausage, smoked salmon, eggs benedict, cheeses, butter ... oh, they lost money on me, that's for sure!
Elizellen is right: the staff are very eager to please. I asked for sugar free whipped cream at dinner one night and they presented me with a big bowl every night for the rest of the cruise! And our waiter learned pretty fast that I didn't want potatoes, rice, etc. on my plate. They are happy to pamper.
Our cruiseline, btw, was Celebrity.
As for water, the ship's tap water is good to drink. Take along refillable bottles for shore excursions -- no need to pay exorbitant prices.