Being a mother of 4, I know how hard it is to take a vacation with or without kids!
Babies are not something that you can turn on or off. As our children came into our lives, we learned how to travel with them. Mostly by car or by plane, back then we could have not afforded such a nice cruise. Nor had we ANYONE whom would take them for us to go on a vacation! It's just too big of a responsiblity that many do not want!
Traveling by boat is no different than traveling by airplane. ActualIy I think its safer (healthwise for him). There is plenty of fresh air at sea, no recirculated air such as an airplane. I am also sure that due to his age (newborn - 1 yr) he will not be eating the same foods as we all do, more likely he is still on the bottle or just hitting the gerbers!
The little guy also probably is not walking/crawling yet, so therefore, he won't be touching all of his surroundings. No chance to come in contact with germs.
You are lucky that at least grandma is there to help out some of the time.
I think he (the baby) will be just fine! Assuming you have checked with your Pediatrician,
I see know cause for alram not to bring him. Ask the pedi if you can use the wrist braclets on him, just incase the seas are rough. They have no meds in them and might aid him if needed. Good Luck, and remeber, they do grow up quicker than you know it.
My first born just graduated for high school and the baby of the bunch is hitting middle school......