I'm assuming the use of a high quality 3.5-4" pocket knife. Granted, I did say minimal, but what I meant was minimal compared to a direct hit. It is a fact that a grazing blow deals far less damage than a direct one. However, with a knife, a glancing blow can result in nearly as bad of an injury. The arteries in the wrist, for instance, if the aim was for the forearm. If you can grab the bat and pull your assailant in, even while sustaining a broken hand, it may be possible to land blows with the knife to the chest, arms, face, throat, etc.
It all depends on an individual's pain tolerance and strength in the end, and like Dan said, there are too many variables.