My understanding of hand damage is that it functions like damage does for melee, but for gripping, it functions more like stab damage. In other words, it gets added after the multipliers instead of before.
In this case, +1 hand dam <= +1 dam, depending on what you're doing. +2 hand dam would increase melee hits by +1 dam per attack, but it would decrease grip damage by 6 or 7 or 8 or whatever the multiplier is (I have no clue actually).
Does anyone know for sure if this is right?