I would wait just to be on the safe side. I waited until Zeus had at least 3 sets of shots in him before I walked him. Parvo is such a dreadful and painful disease. I cared for puppies with Parvo when I worked at a vet clinic and it broke my heart everytime a sick pup would come in.
Yes, you need to wait until he has all his shots! Otherwise you run the risk of him getting sick. Bordatella (aka Kennel Cough) is airborne so it's extremely important that you get that vaccine...also distemper, hepatitis, etc.
Yoshi had a shot that had 3 different things (maybe 4) in it. He also had a banana flavored medicine given through a syringe-like apparatus. That, I believe, was his deworming med. I'll have to check his papers again for exactly what he had. I'll definitely keep him off the ground and all until he's had all his sets.
I thought the yellow stuff was the dewormer. I knew it tasted like banana because I need it too. JK!! . The vet said it did and it was yellow...LOL. I have since learned that Chis love banana with Yoshi no exception!