Most of the schools are probably preternatural, but not obviously supernatural. The schools that are restricted to swordsage and crusader, which are a little more "supernatural" by intent, have more obviously supernatural elements. The schools that warblades use, which is the most "fighter-like" of the 9 Swords classes, are basically "fighter+".
I mean, these are some of the 9th level manuevers open to Warblades:
Strike of Perfect Clarity: | Strike | Deal +100 damage on single attack. |
Mountain Tombstone Strike: | Strike | Attack deals 2d6 Constitution damage. |
Feral Death Blow: | Strike | Leap upon foe, slay him with a single strike. |
They strike me as obviously strong, but nothing that screams "that fighter is actually a wizard".
Link for reference.