This is why being left handed was not an option in the past.
“Théoden then advances his cavalry at a trot to the top of that ridge we see. Each rider ought to have a spear in their right hand (held upright for now) and a shield in their left. “
https://acoup.blog/2020/05/08/collections-the-battle-of-helms-deep-part-ii-total-warg/