Not necessarily a SME, but I have quite a few years of aikido and TKD experience, with some fencing and kenjutsu thrown in, and some (irrelevant to this discussion) shootfighting besides.
I disagree with Markdoc on weapons and speed. A knife in the hands of someone who knows how to use it, and is in range to do so, can make multiple effective attacks per second. That's just not possible with any sword. It's not a question of mass in this case so much as form factor--even Zorro-like slashing with a rapier, which would be about the fastest type of attack possible with a sword, isn't going to be as fast or effective as an escrima- or krav maga-type multiple slash attack against multiple hit locations with a knife.
The rapier's significant advantage stems from its reach, not its effective speed. It's not hard for the swordsman to keep a knife wielder at bay with the longer weapon in this case. It would also be easier to inflict an immediately incapacitating wound with the rapier. But it won't be faster than a knife in any way.