Will Knives of the Night work in daylight, the Godbound with the Word of Night making their own darkness into a weapon even though there is none in the environment?
Unless your skin glows from inside, there is at least a shadow in your sleeves, so you could use it anywhere. If you were unable to use it in light, it would say so in the gift.
My initial response was that he was a bloody demigod of Night and could create darkness out of nothing.
Yes, it works fine under any circumstances. The power generates any necessary amount of darkness to cut people with.