I strongly dislike deliberate, outrage-seeking acts of provocation and disrespect, like drawing cartoons of Muhammad knowing that doing so is seen as an insult by Muslims. I'm against a day dedicated to such drawings because I believe that said day would contribute to hatred, division, and misunderstanding.
That said, I'm also against blasphemy laws because they always result in heavy restrictions on freedom of belief and also because they rely on extremely subjective, preferential, and malleable criteria for determining what is or isn't "blasphemous." We can see what kind of abuse they can result in when looking at, say, Iran or Pakistan, where mere irreligiosity can lead to a death sentence because of being "blasphemous." Realistically, a blasphemy law could never apply consistently to all of the thousands of religions in the world, but applying it only to some religions but not others would be a starkly inappropriate double standard for a state law to have.
I don't think this issue will go away by having a "blasphemy day" or any other special occasion. Most of the Western world has had no laws against "blasphemy" for decades, yet this level of violent outrage still occurs in response to such. In my opinion, the issue will only properly be dealt with at its root when most Islamic countries become more secularized and move away from fundamentalist, hardline interpretations of religion. I don't know whether that will happen in my lifetime, though, and I doubt it will.