I've been mulling over the significance of this effort. Perhaps if we did all draw our idea of this man, over time, the Muslims would become less sensitive about the issue. Or perhaps they will be more sensitive, because we are actively disrespecting their faith. In the Old Testament, Christians too were bidden to make no "graven images" (Exodus 20:4).
I for one have no idea what he looked like, and so if I did attempt the sketch it would be of a caricatured bearded Muslim. Perhaps a halo or some such symbol of his spiritual importance would ease the insult. I don't know. But I do offer to you that this is the day to create your visual representation of the great prophet Muhammed, in protest of censorship, with respect for the man and his path, and in humble appreciation of the complexity of our international and intercultural reality.
Everybody Draw Mohammed Day was an event held on May 20, 2010 in support of free speech and freedom of artistic expression of those threatened by violence for drawing representations of the Islamic Prophet Muhammad. It began as a protest against censorship of an American television show, South Park, "201" by its distributor, Comedy Central, in response to death threats against some of those responsible for two segments broadcast in April 2010. Observance of the day began with a drawing posted on the Internet on April 20, 2010, accompanied by text suggesting that "everybody" create a drawing representing Muhammad, on May 20, 2010, as a protest against efforts to limit freedom of speech. (from Wikipedia 5/20/12)