Can you spread a cold sore to a 4 month old just from talking (respiratory droplet)?

Unlikely: The contact typically needs to be more intimate, usually kissing, sharing a glass or eating utensils, or by touch. Remember that you can also infect yourself. Be sure to wash your hands before going to the bathroom, rubbing your eyes, near a cut etc. You will be contagious until the area is completely healed with no sign of it ever being there.

Yes: This can occur. More commonly by touching baby, but anyone with a cold should stay away from the baby for fear of spreas.