As I have seen said here many times, with S&W, never say "never". However, I will admit that I have never heard of such. I also don't recall off the top of my head that they made any 8 3/8 K frame models with a shroud of that nature. I don't think there were any M19s with a barrel over 6", and that's the only K frame candidate that comes to mind right now.
Where did you get it? Does it look as though it was always a .22, and not sleeved down or something of that nature?
Oh. A thought - what about the .22 Jet or whatever that was - an M53? Didn't they have a shrouded barrel? Did they make any with a barrel that long?
ETA: Looks like an M53 barrel, mis-marked, or a custom marked barrel based on one from an M53 might be the answer, as I see one that looks like it (8 3/8, ramp sight) here:
Gun Library: Smith & Wesson Model 53 .22 Rem. Jet : Cabela's.