More information really would help answer your query.
Certainly the make, model and year of your boat will help with the "staff" at Cruiser's Forum.
1. how available is ice going to be on your
cruise
2. how big is big, how about some measurements
3. where are you cruising
4. what do you eat, what are you refrigerating
5. how many people are involved
6. how is the box insulated, Is it an older boat
7. how is the box accessed, top or side
This information will get you some detailed replies rather than diffuse suggestions.