Hollywood Cemetery has a searchable database on their website. With a name like this I would stress the importance of checking all possible variations that you can think of. I have found Wigginton men buried under names like Higginson, Higgleton, and even Winting!
You might also check the VA Administrations listing of burials at National Cemeteries. If this man was with the Union, there is a chance that he was reinterred at some point to one of these cemeteries. Here again, check all spelling variations that you can think of.
Another idea: Do you know where he was taken to as a prisoner? If I recall correctly, the battle was in the middle of May 1864 and you list his death date as early June. He may have been sent somewhere else and died there.
Good luck!