Well, there is world of warships ...
I know that's not what you're looking for, but the game is surprisingly good and fun.
Then t here is something called Naval Action (plenty of gameplay videos on youtube), seems to be a bit less "arcade" than WoWs and replaces destroyers and battleships with all kinds of sailing ships. I realize that's still not what you're looking for, but it's closer.. somewhat.
Unfortunately I don't know of any game that would give you a full control of ship from that era. There are strategy games but I assume that's not exactly what you want.
I also have to add that by far the most fun naval combat I've played was in .. Assassins Creed
Black Flag and Rogue are both focused on commanding your own warship. Again, not a trireme, but it's something..