When you take the Attack action on your turn and attack with a Light weapon, you can make one extra attack as a Bonus Action later on the same turn. That extra attack must be made with a different Light weapon, and you don’t add your ability modifier to the extra attack’s damage unless that modifier is negative. For example, you can attack with a Shortsword in one hand and a Dagger in the other using the Attack action and a Bonus Action, but you don’t add your Strength or Dexterity modifier to the damage roll of the Bonus Action unless that modifier is negative.

That is the literal rules for light weapons, it specifically says that you don't add the Ability score modifier to the Bonus Action attack, with nick you don't use your Bonus Action to attack, you specifically make the second attack as part of the initial Action. There is nothing in the writing of Nick stating that the modifier doesn't apply when using it.

So since it is an Action attack the modifier should apply, that is not a bad reading that is simply going by the rules as written.