I don't make a big deal out of it, we just leave it behind and ignore it if we can. Border Collies are born shy and most of them grow out of a great deal of it. I have never had much luck trying to make a pup not be scared of something that they were freaking out about. A scared puppy is not a reasoning animal. A good example of this is grooming.
Some pups are really afraid of being brushed or washed.
This can become a major fight. I have had puppies freak out and go into major panic attacks over being dipped for fleas. I have never had a pup not outgrow this fear. Just ignore the behavior, do what you need to do and the puppy will grow up just fine. I don't spend much time teaching my dogs any obedience when they are young.