You’re more likely to catch a cold from shaking hands than kissing, from what I understand. One, your saliva is acidic, then that travels to your stomach is even more acidic. In addition, your esophagus is coated in mucous, although meant to aid in the travel of food, it also serves as a barrier to keep bacteria from the cells beneath.
Two, your hands are disease vectors in a way most people don’t fathom. People tend to touch their faces more than they know, and they also don’t always wash their hands after sneezing, or after blowing or touching their noses. So there’s a decent chance the sick person has cold germs on their hands, which would then get transmitted by touch, then the recipient rubs their eyes or nose.. and voila, the cold is passed on.
I’m skeptical about the person catching a cold from oral sex. I’m betting skin-to-skin transmission is at play here.