Dozens? Then I hope you have some way to speed up combat, or that this is a play-by-post. Could you imagine sitting around while DM rolls fifty attacks?
The only solution to your problem is a magic item (possibly modified from an existing item). If your NPC can make, say, forty attacks in a round and the combat lasts for five rounds, that's two hundred daggers. There's just no way anyone could carry that many in a way that they could be drawn, even if the person is strong enough to walk around with 200lb of metal.
I agree with other posters - modify a magic item. Really, all you need is a Quiver of Elhonna modified to hold 200 items in the main compartment instead of 60. The nice thing is, it could actually be useful to one of the PCs after the encounter. If you want to stay away from custom items, the NPC could be wearing four Quivers of Elhonna. The item should do what you want. It holds things "roughly the size of an arrow," which would include daggers (a dagger is longer than many people think), and you can draw from it the same way you draw from a quiver or scabbard, which means Quick Draw would work.