Actually I do associate Darth Vader with a light saber, rather heavily. Because I grew up with Darth Vader merch, and let me tell you: it was all red, because of the light saber. Darth Vader's iconic image just has a light saber.
And that's fine, because despite that the image of Darth Vader is also not just being a swordsman, we know very well that he's capable of other things. (Mostly choking people one-handed, he does that a lot.) A character is not merely defined by their weapon, and Darth Vader's actually a really good example of that.
Golbez can have a sword without the sword defining him.