Hello,
I'm glad that the methods are working for you, MyDyson. However, I would suggest that you be careful, since I'm not quite sure what you mean by "quick wrist snaps. " A quick and fairly gentle tug sufficient get a pup's attention, a "yank," can actually be better than a snap. A true snap involves putting some slack into the leash and then, WHAM, jerking the leash quickly and quickly letting it go; it is much the same as the way towels are snapped. It really gets a dog's attention and is very effective, but it is also somewhat harsh.
While I think this has its place in getting the training an older pup or an adult dog that is being disrespectful by ignoring important words like "come,"
when he already knows them, your puppy probably doesn't fully understand its meaning yet. He probably isn't being disrespectful right now; that would be more likely if he had previously learned about walking on-leash and the word come, and he was an adolescent puppy or adult dog.
Also, I would suggest that you teach him to walk on-leash before come. Associating those snaps, even if they are just short tugs, with the word come, would not be good for your pup. He needs to think, especially when first learning the word, that come is a very GOOD word. When he is obeying this command, GOOD things happen. The time for corrections with come is later, when he knows the word well and is being disrespectful by ignoring you/not paying attention. (Of course, if you thought he hadn't heard you, you would repeat the command in a loud, stern voice before punishing him with real snaps. They really aren't something to use lightly; tugs work better with puppies.) BUT, when he gets to you, having fulfilled the command, make sure to do something really good: pet him, praise him, give him a treat, throw him a toy, do something that he just loves.
Instead of come, with teaching him to walk on-leash, I would encourage him to come closer: snap your fingers, cluck or kiss to him, say his name in a happy voice. I will repeat: the use for punishment is with a disrespectful dog; puppies that don't know any better aren't being disrespectful. If he is pulling you, I might try giving the leash a tug just as he hits the end of it, before he is pulling. If he learns that he can pull, you will probably have more trouble teaching him than if the notion never enters his head. Another effective thing that some people do is to turn around and walk in the other when the pup gets to the end of the leash; this only works when a pup is still fairly small, because a large dog will just drag you off.
All of this is just my opinion on training puppies, but it does seem to work for me. Our 5-month-old Kuvasz puppy (our first puppy too), Sapphire, is pretty good with come and will consistently run to me off-leash from all the way across the yard when I call her. While she still needs more work, I think she is coming along nicely. With walking on-leash, unless she gets scared, quick tugs are all she needs as a reminder to not pull on the leash. Even when she is scared, one firm tug will usually stop her from running or hiding; I have not found snaps necessary. She is pretty big too, I'm guessing 60+ lbs., since she was about 45 lbs. when last weighed at 16 weeks; the "little" girl could probably drag me a bit if she really wanted to.
Hope everything goes well,
Sofia
P.S. I would consider seriously considering Red's opinions, because she really knows what she is talking about. Or it seems that way.