I have had gobys with puffers and they always have stand offs ending comparable to chiclids establishing dominance.
I wouldn't put in any fish you wouldn't want to lose.
your success might all depend on what puffer you get and when you introduce him into the tank.
Did your gobies get eaten up by the puffer? Which puffer are you keeping?
Introducing the puffer when the gobies and shrimps are big enough so that the puffer don't see them as food would be a good choice. Do you think so?
Another scenario is to introduce them all 3 together (puffer, gobies and shrimps), what do you think?
I have heard people introducing lionfish together with other smaller fishes together so that they grow up together hence the lionfish not seeing the other smaller fishes as food to nom on.
That whole "introduce them together" argument rarely works...and if it works it generally isn't because the larger predator no longer sees its tankmate as food, its because the owner feeds them well. If you put predators in with prey you will most undoubtedly run the risk of losing a fish. a puffer and a shrimp isn't going to work unless that shrimp is twice the size of the puffer.