Book two seats but NOT the infant, only add him if needed on the day of travel. Correct the birthdate of your wife to that of your son (calling in) if it’s just a boys trip prior to check in. Fly with your son impersonating a girl, have a laugh with him about it in later life.
This strategy only becomes a problem when the child is old enough to object to being called the wrong name going through security.
Source: myself undergoing domestic travel switching siblings, replacement kid <2 but occupying a seat.