Most puppies do not have all their shots before a puppy class. Vaccinations are completed at 4 months, the most important socialization period for a puppy ends at 4 months. It is very old school to not have a puppy start until after their shots are complete. Puppies are born with natural immunities from their mother that does give them some protection. In fact, if you talk to Natural Path vet, they will tell you not to give any vaccinations until the puppy is 12 weeks. They will tell you that giving them vaccinations earlier will actually weaken their immune system since their natural immunities will be fighting the vaccinations, which will compromise their system. The natural immunities go away between 12-16 weeks, which is why they recommend to vaccinate at that point. It is also why the vaccinations are completed after the puppy is 4 months since all their natural immunities must be out of the system before the vaccine to be totally effective.
It is always a risk that your puppy may come down with something just like a kid going to school my pick up a cold. It is more of a risk that your puppy will have lifelong problems because of not being properly socialized. More dogs are put down every day due to behavior problems than any dog dies of disease. You should be careful about where you take your puppy but you must get your puppy out. Puppy K classes are the safest way to get your puppy out around other dogs. The dogs that come in are healthy and the floor is disinfected on a regular basis. I just participated in a study with the University of Davis Veterinary school that was studying to see if puppies participating in a puppy k class are any more likely to get sick then those that do not. There are puppies that are up to date on their vaccinations that do not participate in classes and still get sick. The best you can do for your puppy is keep their immune system up the best you can, which means give them a very good diet.
I have been teaching for over 35 years and so far have never had a puppy in my classes get parvo or distemper. I have seen hundreds of dogs that have been poorly socialized and have lifelong problems because of it. I have a rescue now that I got at 8 months, which has improved but will never be super stable because of her poor socialization. I got another puppy at 4 months of age, and it was still too late for her as well. She never got over many fears and it took her a long time to get over things and adjust to new situations. They improve, but you can never replace the importance of the early socialization period. I have a Cattle dog that I got at 8 weeks and have taken everywhere as soon as I got him and exposed him to everything I can think of. I can take this dog anywhere, and he is extremely confident and not in the least bit fearful.
It is your choice but if I were you, I would do a little research about the importance of early socialization before you make your decision. There is a lot of information about it on the internet.