Although the average distribution of nociceptors in the hands, and fingertips especially, are higher than in other places, I believe that the force of the blow from the cane on them may produce a sort of shock effect, which acts like an analgesic, as subsequent cuts felt more like dull thuds, and were not essentially painful.
However, I have spoken to people who had a heavy strap applied on the hands at school, and they tell me that this punishment was cumulative and extremely painful applied to the hand itself, and not the fingertips.