It has been my favourite film for many years, but it was adapted from the novel by Anthony Burgess. Burgess was a brilliant mind, a teacher, and linguist which was where the Droog's coded language came from in his creation. It was a social prophecy but Kubrick put it into horrifying visuals, while Malcolm McDowell played the part to perfection, he never got a better part to match his scariness except as a similar psycho kid in the move "If."
The language they developed was called Nadsat of which the book has a glossary.
You are probably right about Kubrick's use of skinheads as the symbol for the movie characters, the fashion for us all in London back then, even for the earlier Mods was to wear those big steel toe-capped boots, even with suits. The Mods developed into skinheads and were into Reggae and Blue Beat, not the racism of later skinheads across Europe.
Anthony Burgess combined with Kubrick scared the life out of the public and government and they pulled the movie for many years after some copycat incidents across the country.