To the You Standing There Alone in the Dark (or To the You for short) takes place in the Bete Noir Zone or Black Beast Zone, opposite of Sonic's world with Shadow being Sonic's opposite of sorts. In this Zone, the males wear clothes that are colored after their family colors. If you work for the Queen, you must wear Black and Yellow/Gold, the Queen's Colors, however you're still allowed to wear accessories that reflect your family colors, hence why Shadow wears the purple and pink gloves and decorations on his shoes.
I like to think that Sonic feels a little odd about wearing so much clothing, so he's a little shy about it.
Since Shadow wasn't a test tube baby in this Zone, I figured he wouldn't be modeled after Super Sonic, so his quills grew straight down instead.