I was specifically thinking of fencing when I said “handguns, only.” Now, there’s a bit of a question for both of us, it’s possible someone who’s lost their arm could still fence competitively. Neither of us know enough about sport fencing to say “absolutely not” to that.
But, for fencing as a combat style? No, they’re done. The off hand is used a lot in combat fencing, this can be with a parrying blade, a buckler, or some other defensive item designed to confuse the opponent, distract them, or trap their blade or, like a cape or jacket. There’s the distant possibility that they could try anyway, but against a competent foe, they’d be at a severe disadvantage.
If your character is some kind of Jedi master, and they’re drawing on some kind of cosmic enlightenment, then you might have the option to say “screw realism.” But in a normal context, it’s just not an option.
That said, if your character is a fencing master, they could still train students with one arm, and you could have a genuinely interesting character there. But actual combat against a competent foe would be a death sentence.
And, I think that brings an end to the one armed fighter questions for now.