Interesting question. There is certainly not one standard script. A variety of well established scripts have been used over the centuries and in different parts of the Muslim world. Also, calligraphy is an Islamic art form and there are calligraphers today who are experimenting with different scripts in which religious texts are written. I don't think anyone has a problem with that.
However, I think there would be a problem with writing the Qur'an in what might be considered a disrespectful way, which might include transliterating it into a completely different alphabet. Although there is such a thing as good handwriting and bad handwriting, I don't believe anyone would consider a Qur'an invalid just because some of the letters were formed in an unconventional way.