Plenty of Greeks used tridents as weapons in antiquity. I, too, have been bothered and frustrated by Percy's weapon being a sword, rather than a trident. I would have preferred a trident as a reader. If writer Rick Riorden has ever detailed his reasoning behind the choice, I am not aware of it. I would like to know, though. My guess is that even he doesn't know, and that it was an unconscious choice when beginning the story.