Ollie,
I don't think there are any dangers in grounding the green wire, there may be dangers in not grounding it.
The question you should be asking is if the PJ sees ground via the interconnecting cables between it and your DVD player. Even though the DVD player may have a 2 prong plug, the processor/receiver that it is connected to may have a three prong job. In that case the coaxials that connect everything may be grounding your projector. You can check this with an Ohm meter. With the power plug pulled on the Sharp check for continuity between the green wire and the ground pin in your electrical outlet. Make sure all the other components are connected and plugged in. If it is an open circuit then you should connect the green wire to ground for sure so the PJ is grounded. If it is a closed circuit then the PJ is seeing ground. I would double check by disconnecting all the connections to the PJ. This should cause the circuit to read open and now you know that the PJ is seeing ground via something else in your system. In that case you don't have to hook up the green wire, but it won't hurt anything if you do.
John Moschella