As I recall, some grammar books recommend using the pattern of "someone hit someone else on the shoulder/cheek/arm etc." while avoiding the use of "someone hit someone else's shoulder/cheek/arm etc."
I did a search in Google Books. There are indeed some but not many instances of "he hit my shoulder/cheek/arm".
Does the latter use sound unidiomatic? Or, does it carry a different connotation?
Both phrasings are correct and idiomatic. There is a subtle difference in emphasis, though. Including on the places emphasis and attention on the location, as opposed to the action of hitting. This makes the action seem more ordinary or routine, because the listener treats it as a matter of course. Conversely, without the preposition, the location is supplemental, and the most important information comes from hit.
This shifting of emphasis away from the verb can be used to signify intent, as T Romano noted in the comments, though of course that's not the only possibility; it can also be used to make a statement more formal or informational by adding linguistic distance, for example. Or perhaps the location was particularly unusual, and we'd like to draw extra attention to it.
A related aside: there's a parallel difference of emphasis when choosing between on and in for use with hit or strike. Again, on is more informational, while in either literally indicates something entering the body (such as a bullet: he was shot in the chest), or by suggesting force strong enough to move through the person. He was struck on the chest suggests a hit that bounced off, while in the chest conveys something stronger; maybe he doubled over, staggered, or fell backward.
As @TRomano states in his comment, they are both in use; neither sounds unidiomatic.
I must respectfully disagree over the implication that in/on implies intent, however.
I live in the south western united states, and I will commonly hear newscasters say something along the lines of "Debris from the wreck struck an audience member in the chest..." as much as I hear things like "Mountain lion mauls hiker's arm...", so perhaps that connotation is reflective of a local dialect.
