We cruised Mexico in Jan. and it was not warm for the first two days until we got farther south. On a four day cruise you may not hit any hot weather. It wasn't freezing, just not swimming weather, take a sweater.
I'd also consider taking the six pm seating for dinner. Aslo consider requesting a table for the three of you. Some people will not want a baby at their table.
We cruised carnival and I just ordered normal food ( no sauses) and cut it up for my 2 year old and I brought a food grinder( they are great).
Talk to your doctor about the medicines for babies. I brought baby tylenol, and baby gravel.
Some people have brought small inflatable baby baths or pools and put them on the floor in the shower to bath the baby. We just held the baby in our arms when one of us showered and the other one helped wash him. It's only four days. You could sit him in the sink and do a spot wash also.
I wish you luck, but don't expect it to be exactly easy with a baby, at least you won't have to cook or clean though!