Well in that case it should be noted that the sword was not the preferred weapon on horseback. That honor belonged to the lance, and you lance across the body so it’s the horse on the left that has to worry, not the horse on the right.
Actually, it was the same on foot. The sword arm was furthest from the opponent, not the closest. The shield was closest to the opponent, not the sword.
So I’m guessing that you just made this up.
We aren't speaking of the battlefield anyway, but just an ordinary road running between villages, or towns, or castles.
The English ride on the left, and the French ride on the right.
It all depended on how much risk there was on the roads.
So, how much risk was there?
You could bother looking up "Why do we drive on the right" and you would find gazillions of references. One of them is the Wiki piece ~ which can serve as a guide for you.
No, I didn't make any of this up ~ it's just your imagination that I could have and that's a tribute to my writing ability.