It's well established that the tetrodotoxin in pufferfish can be deadly when ingested, and there are numerous reports of accidental poisonings involving improperly prepared fish, but as far as I can tell, the danger is from eating them, not from handling them. Their spines don't have any mechanism for injecting venom (unlike, say, lionfish) and I can't seem to find any reports of anyone being envenomated by merely touching one.
That said, they have strong beak-like jaws—adapted to crushing the crustaceans they prey upon—and are reportedly capable of inflicting nasty bite injuries, so you probably shouldn't try holding one in any case.