My guy wears a sport coat and tie. On our last Carnival cruise in December (Triumph), everyone was so casual, even on "formal night" that he just wore a nice shirt and his sport jacket.
We've also cruised on Princess, NCL, Royal Caribbean and others ... and he takes the same thing. I think Carnival is more relaxed.
The men in tuxes look sharp, but my fellow is more comfortable in his sport jacket or suit -- personal choice in my opinion. He AND you will be comfortable either way!
Enjoy -- after your first cruise, you'll be planning another! :dance