How do you know he doesn't fit the Swordsman type. He has a sword all the time and we see him using it edd war and vs WB. We see him doing air slash.
"A swordsman is someone who is at his strongest with a blade" that would also apply to Whitebeard. Whitebeard with a bisento is stronger than without it. Though I think Whitebeard with a club would be just as strong as with the bisento (assuming the quality of the club is the same).