The Daisho Expertise feat says:
Prerequisites: Proficiency with the katana or wakizashi.
Benefit: Increase the damage die of katanas and wakizashi you wield by one die step. In addition, you may use your Dexterity modifier instead of your Strength modifier when making attack rolls with either weapon. This feat counts as Weapon Finesse for purposes of meeting the prerequisites of other feats.
Special: If you are proficient with the katana as a martial weapon, you meet the prerequisites for this feat, although you only gain its benefit while wielding a katana in two hands (to gain these benefits while wielding the katana in one hand, you must possess Exotic Weapon Proficiency with the weapon). You must possess Exotic Weapon Proficiency with the wakizashi to gain the benefits of this feat with a wakizashi.
At first level the weapon champion selects a group of weapons (from the fighter’s list of weapon groups for the weapon training ability) to act as her favored weapons. She is proficient with all these weapons. If the weapon champion has a feat that applies to one of these weapons (such as Weapon Focus), it applies to all the weapons in the group.
The wakizashi belongs in the light blade group.
Does the Weapon Champion's 1st-level feature now make all light blades use the Dex stat to hit and treat them as one die higher for damage?
Because as far as I can see, it the wakizashi fulfills 2 criteria, it belongs to the light blades group and is part weapon-specific feat that can apply to the shared weapon group.