You're not suppose to sharpen mechanical pencils.
A mechanical type sharpener is one that has a handle that you turn.
I believe you are asking about an electrical sharpener, right? Just keep jamming another pencil in it, eventually the lead will come out.
I don't know if it is technically possible, don't know if it records from the satellite feed or from the tv. If it is physically possible I don't believe it would be illegal.
I would feel more relief if Israel let the Palestinians alone, stopped the blockade and gave back all the land that they have stolen over the last few decades.