Is it possible to trace bitcoins, not via sending/receiving adresses but the the coins themselves?
There is no such thing as a bitcoin, so there is nothing to trace.
There are only transactions. Transactions spend previously unspent transaction outputs and create new unspent outputs. For the standard transaction, an output is essentially an address and a value.
I reckon the smallest denomination (a satoshi) would have to be represented by a unique code in the blockchain to prevent double spending and other issues, is my assumption correct?
No, your assumption is not correct. I suggest that you read the Bitcoin Whitepaper published by Satoshi Nakamoto before you try to guess how bitcoin works.
How would I be able to trace coins?
Since they don't exist... No.
