I had the same idea and was convinced by a biologist, that his is a very bad idea. To be able to spread, this vaccine-virus needs to infect the people vaccinated. Any infection is dangerous, as it means the virus is multiplying in your body until the immune system hopefully takes hold of it. What happens if it doesn't? This happens with traditional vaccines all the time, but the consequence is only that you are not acquiring immunity, no other harm done.

The other point is, you have made a completely new human-transmissable virus. How do you reliably prevent it from mutating into something more dangerous?