This is such an easy one! NO, HSV 1 is not transmitted in the way that you describe. There are infections that are spread by droplets such as you describe, like colds and flu, not NOT HSV.
Have a great Thanksgiving!
Also, have you actually been tested to know that you don’t have HSV 1 infection? The majority of the US population is, and the vast majority don’t have symptoms or symptoms that they recognize.