Surprisingly copy him, red under the skin (10)

'skin' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Perhaps there's a link between them I don't understand?

'surprisingly copy him red under' is the wordplay.
'surprisingly' indicates anagramming the letters (a surprising ordering of the letters).
'under' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'copy'+'him'+'red'='copyhimred'
'copyhimred' is an anagram of 'HYPODERMIC'.

'the' is the link.

Can you help me to learn more?