Speed and accuracy kills. If I can avoid it, I don't even like to parry. Rather take or check the hand if I can. Avoid if I can't. Parry, trap or deflect if I must.
Speed and accuracy depend on practice , No matter the tool you practice with it needs to be the one or exactly the same as the one you fight with . changing hands and positions in the hand take practice and with that ,skill can be developed .It's not automatic. When I train some one to shoot ,I emphasize learning to use both hands independently . The same with sword and knife fighting, being another person or an animal you are engaged with . Predators fight with either paw ambidextrously, they must to survive . If you are predominantly right handed, and it is severely damaged then what ? I don't see the need to write with the non dominant , but I believe that it is valuable to be as ambidextrous as one can be .
I have fought bated blade matches against Korbschläger's against fellow SCA members with a dagger and boarding axe it's an interesting combination that combines speed with the dagger and strength with the boarding axe... for an old fat man past his prime it's a pretty good combo...
When I took fencing it was the little guy that had the advantage. Of course those were foils not broadswords. My son and I would spar with broadswords too but it's expensive because the eventually break .
I stared with a broadsword, moved on to a katana for about 5 years, then 7 with a butcher saber, and then moved into German longsword and Highland basket hilt. With a bunch of random weird crap in the middle. No safety measures,honestly it's a miracle everyone is still alive at this point. VERY different results than the "safety" sparring I have come into contact with over the last few years as legitimate martial arts groups have finally moved into the general area.
True. We train with both hands and change up what we have or don't have in each hand. Harder, but better for your brain too.