Azamara is 'country club casual'.
How about Ocean Village or Island Cruises? Most GOOD cruise lines DO require dressing up. That is WHY they are good! Football shirts and baseball caps always seem to be the dress of choice on cruise lines that describe themselves as "informal"! It is your choice.
NCL is freestyle cruising,so you can please yourself whether you dress up or not.
I had years of cruising and dressing up for meals in the merchant navy. I found that being 'dressed up' didn't improve the food, service or surroundings. :-) I don't own a football shirt or baseball cap so looks like informal is out as well.....I don't mind a suit and tie but I draw the line at dressing like a penguin.
I think you'll find that wearing a suit and tie qualifies as 'dressing up' on most cruise lines these days.