The genesis of this issue was in the early 70s. So I can only repeat what my friends who were LE officers, armorers, and in the gun world then (when I was in short pants) taught me in that regard. I have a pair of 66-1s and a 19 that I care about keeping in top shape, so I've researched it a great deal.
In the 1970s, there was one particular 125gr .357 loading that was widely used by LE agencies. The loading was from Super-Vel. It was a high-energy enough round that the thin forcing cone on the bottom of the barrel could be induced to crack. This has been documented by a number of gunsmiths, armorers, journalists, etc. I believe Ayoob wrote one particularly prominent article in the late 70s on this issue that sparked debate and got it resolved. That particular loading was discontinued/modified, and the problem has disappeared in commercial ammo. I would wager, however, there are handload recipes out there for 110 and 125gr rounds that can replicate that unique Super-Vel round, or you can find it in older manuals (I bet some of the loads in my Speer #8 could do it!). So stick with modern commercially loaded info, or modern handload recipes. Also, the issue is more pertinent to 19s than to 66s because of the metallurgic differences in carbon steel vs. chromium steel (stainless). Anecdotal gunsmith data I have run across says it was about 5:1 an issue of 19 vs. 66 guns. (Recall also, 66's didn't come along until the early 70s - '71 I think - so many more 19s were out there in service).
This was one of the reasons that S&W began to develop the L-frame in the late 70s (introduced in 1980). I am told any MODERN 125gr. commercial loading in .357 is going to be ok for occasional use in your K-frame without worry - the offending load has been long gone from the market. Again, this is not my personal data but from industry professionals I know personally or have read detailed articles/posts from. I trust this information based on their credibility, and the lack of contravening data.
If you examine the forcing cone of your K model, you will see the barrel is cut horizontally at the six o'clock to allow clearance for the cylinder crane. This compromise was fine in 1899 when the K model was designed around the .38 special round. It worked acceptably with .357 rounds for a long time (15 years) until the one light, really hot round came out, and was unfortunately widely adopted and fed through the gun in volume.
Personally, I don't feed the "little rounds" through my guns - with magnum rounds I am more interested in wound cavity and expansion, and the penetration of 158gr. is usually more than adequate! 110gr and 125gr. rounds just don't have application for my uses. I would use modern ones (110, 125gr. were I forced to by circumstance). But I don't use them in any gun I own, much less my K. When I feel the need to deviate from the conventional 148 to 158 or so grain conventional bullets, I usually go towards 180gr. or even, gasp, 200 gr bullets, but not down to 110gr.
The other empirical fact that supports the above scenario is the total LACK of fractured K frame .357s showing up in gunsmith hands these days. It just doesn't happen. Occasionally, an old gun gets dug out of a drawer and sold with problems, but it's from the '70s, not a new issue. No one has been able to credibly report a "new" incident of K frame cracking since the mid 80s.
I DO pay attention to this because I also like old ammo and guns. To demonstrate that, I'm going to violate my rule of never posting pics, but here's a pic of my 1970 S&W 27 3.5" with contemporary "metal piercing" winchester ammo:
Hope this helps the discussion.