Welllll, maybe.....
............but I bet SmithNut would know.
Wow, that's a tall order/expectation

When it comes to S&W's, one must remember to
Never say never, as wierd and unique stuff shows up all the time.
If the question is "Did they ever produce a standard
production model K frame, short barrel 22LR in any volume", I'd have to say no, never heard of one.
If the question is "were there ever
any produced, then my quess would be a qualified
maybe.
Here's a for instance, the pic below shows a (IIRC) 3.5" SB K22 in the lower left. This gun was made for Ed McGivern, along with the other guns in the pic. The gun above is is a 3" M&P Target in 38 Special with RB gripframe made also an Ed McGivern gun, now that is a really cool gun. These guns are all owned by a forum member (Mike P) and he was gracious enough to let me look at, fondle and photograph them a couple years back, a big thrill.
One off guns from the factory do exist, many do letter as shipped in unique barrel lengths and configurations, it's just that you don't run into them all that often as many are in collections of advanced collectors.
Here's a pic of some pretty special McGivern guns, with the K22 in the lower left (7 o'clock position).
Enjoy (I did

)