Yup, I meant Drex the Klingon son rather than Krax the Ferengi son. Sorry about that!
But the Earth tradition on challenges is that the one issuing the challenge is not at liberty to choose the weapons - if anything, the party being challenged is, but that's a somewhat rare interpretation of the "rules". Generally, the two sides will come to some sort of an agreement about the terms of the fight before the fight takes place, but with so many variables there that Klingons would no doubt grow weary of the proceedings and slay everybody involved. They have never been shown discussing the terms, or arguing about the choice of weapons - but sword is countered by sword rather than by disruptor or starship, so presumably the Klingons have ideas about this. It would appear a bit unlikely that a "nerdy" strategic genius would get to choose a weapon allowing him to defeat a master swordsman.