Of course, if you just drive by the checkpoint and don't stop, I doubt anyone will notice. We took our goats into Utah last year, completely forgetting we might need health papers. So we drove past the border checkpoint and hoped we wouldn't have any reason to be stopped and questioned about out-of-state livestock. We actually got away with it just fine and no one gave us any bother, but it would have felt better if we'd had the necessary documentation just in case. I wouldn't want my goats to be impounded!
Each state differs but you can get a general health certificate from a vet for very little money. All they do is a look over and sign off on it. But like Nanno said and if it were me, I wouldnt even stop. There really is no reason to. Your goats are going to stay with you and come back with you. They main reason for health papers is to be able to track a sickness back to this origin. Much the way scrappy tags work and is usually only done for the sale of an animal.
Here is a key piece of info if you do decide to get a health paper. First call your vet. They will be able to call which ever state and find out exactly what is needed. Also, if you dont want a metal tag in your goats ear, you will need to have it tattooed so that anyone inspecting the paper can match it up with your goats tattoo. No other form of personal animal id is accepted that I know of.
The state of Montana agreed that I could use the microchip as permanent ID. In fact they noted it as "an excellent idea". The Oberhasli has black color skin in the ear so a tattoo does not work so well. These were not sexually intact animals so it was a little easier.