As a left-hander, I've come to the conclusion that many people regard left-handed fighters with truly superstitious awe. In the 16th century, it was quite common for a left-hander to be required to fight a right-hander right-handed so as not to have an "advantage".
This is just nonsense. It is only against inferior combatants and the superstitious that a left-hander has any significant advantage. Thus, how to realistically portray the effects of being left-handed in melee combat?
I pull together a few things.
First, being left-handed qualifies as a "style" in the Martial Arts sense. That is, anybody who is unfamiliar with left-handed fighting takes the -1 active defense penalty until familiarized with the "style". Left-handers do not automatically begin play with familiarity to this style -- they had to have faced other lefties to get it and must purchase it the same as anybody else.
Note that any creature that fights instinctively (animals, etc.) does not get this penalty. Only creatures that have trained how to fight in a context where handedness might matter are effected by this.
Furthermore, there is a new mental disadvantage:
A lot of mediocre fighters have this disadvantage.