Is that your own interpretation or the band mentioned that somewhere? I mean, I understand the representation of the shadow as one's dark side but I am more interested in the actual image of a man without a shadow.
Who is, or rather what is a man who casts no shadow? A ghost, a vampire, an undead in general. If this is so, then they inherently have no soul and the lyric would then be just as pointless as finishing the song with "Today is Saturday".