Knives and Katanas both scale off of strength. Testing the basic attacks and skills of the "SwordTech" and "RogueHand" programs between a character with 4 strength and a character with 20 strength always yielded marginally higher numbers for the character with 20 strength.
I did these on both a katana and a knife with a base weapon attack of 12. The base attack of the weapon also has a pretty significant role in the damage as well.