I expect that any prime would work, but most zooms would not at the widest end. I just tried a shot with my f/2.0 24mm on my D300, and there was not a trace of a shadow. Switching to the f/4.0 12-24mm at 24mm there was a shadow with the lens hood on, but not if I removed the hood. Zooming wider with the hood removed, the shadow appeared around 17mm but barely perceptible. Of course, at 12mm it was profound.
Another alternative would be to buy one of the shoe-mount flash units. That would bring the source of light considerably higher above the lens, plus they are capable of bounce flash, which would eliminate the problem entirely.