Sorry to bump a dead thread but I THINK I have an idea. How about this.

Level 3: Expertise on Perception, add Wisdom modifier to katana damage.

Level 7: May draw sword as a bonus action, first attack after drawing sword crits on 19-20. Add Wisdom modifier damage to this attack if it crits. If it kills the target, the next attack benefits from the same bonuses.

Level 10: May reflexively sheath sword at the end of a round. May roll initiative with Wisdom instead of Dexterity.

Level 15: May attack again after killing an enemy with a critical hit, up to Wisdom modifier times per long rest.