I don't know whether Nikon makes a flash wide enough for this
application. Pentax's AF 360 FGZ will cover the AOV of a 16 mm
lens in APS-C, 24 mm. in 35 mm. format. There's also a fold-down
diffuser panel for wider angle. I don't recall how wide it will
diffuse the light.
Solutions: A Stofen Omni-Bounce. Something equivalent. Something
home-made to diffuse the light. Available light.