As a vet, I get this question quite a bit!
The chances of you getting infection from your dog are quite slim. As long as he is getting regular check ups then you will be fine
Stray dogs have a higher chance of giving you an infection. If you are still worried then here are some things you can do to clean his mouth.
- Get a brush and gently clean his teeth and gums
- Have him drink some water
- Regular dental sticks (They are cheap!)
- Simply take a shower after you are done playing with him.
Let me know if you have any other questions. Have fun!