After years of shaving I have the act down to the minimum amount time due to not having it high on my priority list. Of course the shave(boss) vs. don't shave(daughters) debate is more of a hassle then shaving itself.
A more interesting question is "Does the dominant hand of the shaver dictate which side gets shaved first?"
When reading your post I saw you as left-handed as I am and I always start with my left jaw area.
Of course another one of those "bizarre" questions I have pondered is "Which side of bed is dominant for the respective sexes in the marriage?"
I have noticed that out of the family of 7 and a half dozen friends(couples) the male is on the right side(standing at foot of bed looking at headboard) 10 out of 12 instances. With the side of bed nearest the door being the male side if applicable.