Give an option to select "left/right" handed for your character. Then flip all the animations that character has. Sword and board holds the shield in the right hand, lancers hold their lance in their left. 1h left hand spam becomes right hand spam, chambering someone's right swing as a polearm leaves you with a good swing animation, rather than a borked (current left swing) animation. HX/HA can turn their bodies opposite the normal direction without screwing up their aim, etc...
If you've ever dueled someone who uses inverted mouse swings, you'll notice they're somewhat less predictable than others and are also harder to chamber. While this might not be anything like that (aside from cav vs cav, maybe) it basically doubles the amount of animations you have to watch for. Maybe rather than having it be a website option, have it something like an "alt mode" where you press a key, and you change your holding of the weapon immediately, from right hand dominance to left.
I think of it as something like a rightie boxer facing a lefty. Who knows, it might actually add a bit of depth.
Edit: Maybe allow people to switch hands in game for a wpf penalty?