I think it would be best if you contacted the cruise line directly informing them of your son's nut allergy.
Do you normally take him on holiday to foreign countries and stay in hotels? You are basically "eating out" at every meal if you go on a cruise. Although the cruise lines do cater for most diets, and would no doubt do their best, I am not sure that I would choose to expose him to such mass catering on a prolonged everyday basis. I don't know how insurance companies would treat this situation? Have you spoken to any cruise lines, and what do they say? Hopefully someone who actually has a nut allergy and has cruised will pick up on your question.
Yes most cruise lines can accommodate any diet but they add Cannot be guaranteed,he should be ok but ask the waiter before you order his food and take the same care as you would when going out for a meal at home?