I have only been on a cruise once. You can get plenty to eat on fruits,veggies and plain meats. I was always able to find some chicken breast by asking the chef if they didn't have anything else out. For breakfast you should be able to get eggs, bacon and/or sausage. Often they had a Mongolian style grill that allowed me to select the meats and veggies they put in my bowl. This was perfect! They had shrimp, chicken and beef.
So, you should be able to survive if you can resist the urge to grab the other stuff that's out there.