Please don't do things to make your pup distrust you and be afraid of you...what you'er going to do next to him. This undermines the developement of a good, trusting, bonded relationship with your dog. You don't have to do these things to your dog. Why is everyone always searching and trying to come up with schemes of what they can DO to their dog???? Squirt bottles, noisy, frightening sounds, jamming fingers down their throats? What is the deal here? Why is everyone afraid to teach their dog unstead of making their dogs puppyhood miserable?
All you have to do is end your involvement and playtime with the pup when he bites. Remove whatever it is he is getting out of it that he likes and reward him when he is not biting. The behavior will stop when there is nothing in it for him. Grabbing at his mouth he could be mistaking for more play. Hey, it's attention, isn't it. If you have to give a short time out when he's terribly rambunctious, do it...calmly and quietly. Show him that playtime is over when he bites. Give him suitable teething toys for his sore gums. He's a baby. Read the stickies about puppies. See what is normal. Read the stickie Adrienne put up in the training forum about how alpha wolves behave and how to get your dog to respect you. Attacking your dog will not make you look very secure in yourself as a leader.
I've trained so many dogs this way and that's all there is to it. It's simple, quiet hands make a tranquil dog. (and horse) I never had such problems. Puppies chew and nip for a while but they get over it when there's something better to chew on and when you are not available to chew on or play with.