Hmmmm, I don't know, but here are some things to think about.
How would you obtain the vaccines? Seems to me that you would need a prescription. Perhaps, but I doubt that your local pharmacy stocks vaccines for pets. While they may be available at other sources, such as pet supply establishments, you would still need a prescription.
That would need to be obtained from a vet. While it is probably possible, no doc worthy of their salt would write a prescription without first having examined a patient. A doctor familiar with a patient's history and condition may write or renew prescriptions, but other than that, I don't know.
Syringes are a similar concern, as is the skill necessary to administer the shots appropriately, whether they be subcutaneous or intramuscular.
Some dogs don't even flinch when they get vaccinated, others can be traumatized by needles. It's better that they associate that with the vet's office than run away from you whenever they see you with something as innocuous as a dinner spoon in your hand.
Also, keep in mind, that when a puppy is brought in for shots, they get a routine exam by the vet. Their weight is recorded, their hearts and lungs get listened to, and they get palpatated to detect anything abnormal.
The vet will, or should, pay attention to the condition of their coat, nails, eyes, temperament, etc., looking for symptoms that you or I might overlook. They will usually request a stool sample to check for worms and parasites such as coccidia.
They also, or should, ask several other questions, regarding housebreaking, eating and sleeping habits, and how they are getting along with other family members, including other animals/pets.
These visits also serve to acclimate a puppy to a vet's office. A good vet will spend a bit of time on the floor with a puppy, making friends with it. This can establish a "rapport" between a vet and your pup, which can serve you and your dog well should they require the vet's attention in the future.
Just some food for thought.
Tom