At Expert Dagger, you can wield daggers in your off-hand (and something else in the main hand). Similarly, at Master Sword, you can wield swords in your off-hand.
However, if you don't use Grayface's patch, it doesn't make too much sense to use it, since your resulting attack time will be equal to the sum of attack time of the both weapons. So you will be very slow and your "damage per time unit" will actually drop (or at best stay the same) by dual wielding. With Grayface, the attack time is just the larger attack time of the two, and it starts to be viable.
(Fun fact: when you obtain Blasters, you can dual-wield Blasters with Swords or Daggers, and the melee weapons do count towards the total attack and damage! So imagine a blaster rifle with a dagger of The Dragon, for instance...)