Using "NC Troops, 1861-65; a Roster" I eliminated those in the CSA who enlisted after the death date you gave. That leaves you with:
w.h.King, residence and enlistment location not listed NC 26th Inf, G
w.h.King residence?, enlisted New Hanover NC 3 Cav, A
William H. King residence ?, enlisted Bladen NC 18th Inf, K
William H. King residence and enlisted Randolph NC 22nd Inf, I
William H. King residence and enlisted New hanover NC 1st Lt Artillery, E
William H. King residence and enlisted Stokes NC 21 Inf, F

You would have to check with the NC Archives to see if they could give additional details. It is doubtful they would have any genealogical info, unless a pension was provided due to his service, and that might have genealogical data.