1- do you think Edmund from King Lear would be any good at swordfighting/fencing?

...

2- if so (and I know you'll say he is) (because its his type) then how did he lose against Edgar in the final scene?

1- yes 

2- Ok so.

Let’s not forget.

That he literally stabbed himself, probably in the arm, a few scenes ago.

He’s literally fighting Edgar with a stabbed arm.

I’d assume stab wounds don’t heal that quickly?

It’s kinda karma, in a way. He stabbed himself to frame Edgar, and then he gets stabbed by Edgar because he stabbed himself. At least that’s how I personally see it.