You pass a law:
- Requiring vaccinations, or a $800 fine
- Permitting private venues to verify vaccination status by looking at vaccine cards (e.g. employers, concerts, etc.)
- Make it a crime to forge vaccine cards
- International travel already has yellow vaccine books, and it's well-established to check vaccines upon entry to/from high-risk countries
You don't implement any infrastructure to track vaccinations. I show my vaccine card when I enter a concert, same as I do when ordering alcohol. No one records anything.
The bar for intentionally breaking laws is much higher than not getting a vaccine. I think most people will follow laws voluntarily. Most of the ones who don't follow the law won't get caught, but a few will.