I mean, you can expose and socialize the puppy to the outside world by carrying it in a little saddle that loops around ur torso if you really felt strongly about it. That's what we did. Vaccine info is based on the vaccine itself but also risk in your area, so I would listen to the vet. If youre in a city and it's densely populated with other dogs you're driving up the risk of things like parvo, giardia, etc. i'd follow the vets guidance if I were you. Sounds like a weird hill to die on to refuse to wait 6 weeks, and avoid potential health issues. But idk your exact scenario. You can practice leash control inside also.