The dancing is just as much gameplay as sword fighting. I'm not sure why it's being singled out. Then again I found the game too easy to complete on my last Swashbuckler run through this Summer, so I might not be typical.
The name of the game is, as you said, not losing a battle. Losing a battle means losing your ship. Losing your ship means losing your Large Frigate. Losing your Large Frigate means you can't invade various colonies whenever you please, and losing the ability to do that makes it more difficult to earn promotions, which are generally the last progress I complete.
By focusing your efforts on killing Marquis Montalban earlier than later in your career, you dodge the only possible difficulty, which is beating him in the duel. It can be extremely difficult in later life when you're slow, as his thrust and parry are godlike.
Until you reach that point though, you just sail to and fro chasing Baron Raymondo, capturing every ship you encounter, then selling them, getting promoted, dance, get a map piece, sack the city, install a new government, get promoted, dance, get a map piece, and move on to the next city. The only time I'm not doing this is when I have too few troops, in which case I skip a city or two along the way, or when I'm trying to keep my crew small so they will sail longer without mutiny.
All the other objectives, treasure, pirates, and fugitives, are distractions. You'll sail by them eventually, just focus on the Baron and sink/capture everything along the way.