This puppy has already been traumatized by being removed from the litter too soon, your suggestion will only add to the problem. It's a great way to create a lifetime problem from a temporary one.Get a squirt gun or a spray bottle; fill it with water.
When boundaries are crossed, squirt puppy in the face. Re-enforce with a stern "NO".
Distract the pup with a ball or another of their toys, soon enough, no more bleeding.
Went through a similar deal with a pup myself, still have the scars to prove it.