It can be done! I was on a cruise last August - and there are always low fat, low calorie options available.
For breakfast we usually had room service deliver it to our cabin and ate out on our balcony - hot oatmeal, fresh fruit, coffee or tea (and muffins/danish for dh!). YOu can have eggs cooked whatever way you like (poached/hb, etc).
Lunch can be salads or check out dining room menu.
Dinner can be trickier due to sauces, and obviously you won't find brown rice or whole wheat pasta - but baked potatoes, salads and veggies with a protein (chicken,fish, beef) can be adapted to core (dressing on the side?).
Dessert is harder - if you can resist more power to you - you can probably get fresh fruit or just try some of the other choices - they always had a sugar free option on the dessert menu as well!
good luck and happy cruising!
Frouf
P.S. What ship/line?