You said the vet told you to "wait it out" and I get why that feels weird. But you're kind of missing the point about why they said that. Saltines are mostly flour and salt, and a dog that size can handle that much sodium without it being toxic. The real danger with dogs eating stuff like that is if it causes a blockage, not salt poisoning. The wrapper is what would worry me more than the crackers, but since he passed it or threw it up without issues, he's probably fine. Vets don't just say "chill" to mess with you, they do it when the risk is low and the cure would be worse than the problem. If he was a tiny chihuahua or ate a whole bag of raisins, that's when they'd say come in. You did the right thing calling, but trusting the vet on this one was the right move. Just keep an eye on his poop for the next day or two to make sure that wrapper actually came out.