Vs. A very heavy sword and an unskilled combatant, I'd use a light dagger, wait until they stumble from the weight of the sword, and go for the throat.
You realize anyone who would use a sword also wears armor, right? A simple chainmail coif makes your dagger useless. The sword (primarily the claymore) was actually more useful due to its weight, as it crushed an enemy, not cut him, which would be nearly impossible due to the amounts of armor they wore in the first place. Not to mention knights trained day and night in order to not be slow in their actions. They're not Silent Hill nurses, shambling around like handicaps, they're highly trained military.

Good luck stabbing him. Even if you knock off the helmet and maybe the chestplate, they're still protected by a layer of chainmail on most of their body. Literally, your
fists are a better weapon at this point.