According to the Qur'an and hadith, Shaytan is an immaterial entity who affects people through influencing their hearts and minds.
(By "immaterial", I mean that he is not composed of the same physical material as objects around us. The Qur'an and hadith say that humans are composed of earth, jinn of fire, and angels of light. The prevalent understanding from the Qur'an is that Shaytan is a jinn, although there is a minority view that he was created as an angel. So he is made of something, he is just not made of the same physical substances that we interact with.)
Qur'an 6:122 speaks of shayateen (those who serve the interests of Shaytan) who are humans and jinn. This indicates that human beings themselves can carry out the will of Shaytan without him actually being present in physical form. It also indicates that, when it comes to Shaytan and shayateen, there is a real division between human and non-human beings and it is not metaphorical.
In any case, from that, it is clear that Shaytan does not need to be here in human form to do the job. A commander who can send a footsoldier does not need to show up himself.
In fact, human beings do not even need Shaytan to cause evil! We have the capacity for immense good and immense evil on our own.
There are some rare cases in the Qur'an where immaterial entities briefly appear as humans, such as when the angel Gabriel appears to the Virgin Mary, but it is not the norm.
Also, Allah protects the believers from Shaytan.
So while there are some humans that I might identify as Shaytan (no names here!), the Qur'an lends itself to a more literal interpretation of Shaytan as a wholly non-human being rather than as a someone who is a human or walks around in human form.
