He does look like a show cocker to me, but like you say his coat is more like a worker.
It's possible there is a bit of worker in his pedigree somewhere or he could just be a short coated one. I wouldn't worry about it or what other people say. I had someone swear blind that my last cocker was a poodle
Who cares if you're happy with him.
Either way, he is gorgeous
and the short coat is an absolute blessing in this weather. I'm having to bath my hairy boy every day at the moment