Agreed - most likely artillery (there were more of them) but also correct for pioneer, telegraph, aviation and other technical troops. Enlisted/NCO walking out dress cap, private purchase. Missing the sweatband, which had a tendency to come loose from wear, since sweat is salty and salt is corrosive. Ironically, the ersatz bands were more durable than the thin leather ones under heavy use (for this reason).
I suspect one or the other cockade is replaced. They worked just like pickelhaube cockades - two-piece versions for officers/senior NCOs and one piece painted versions for enlisted. Usually not mixed and matched like this. For an officer, the black band would be velvet so I am guessing the Württemberg was added to replace a missing one. Importantly, it looks mostly moth-free. A nice piece!