"Ok, count me confused, these were originally chambered in 38 LC, a 12,000 CUP round. A 38 Special is a 17.000 CUP round, is that safe to shoot?"
Yes; that gun is overengineered and more than strong enough for the original .38 Special. The cylinder is the same as the OP and is actually thicker than that of a K-38. For many years, there have been dire warnings about not shooting .38 Special in those guns put out by folks who apparently were not aware that Colt actually made the later ones to take that round.
I will say that I don't recommend any extensive shooting of those old guns with .38 Special or even .38 Long Colt. They are old guns and further are prone to parts breakage with few parts available and few gunsmiths who can work on them.
At that time, the .38 Special was the "new thing" (we all know about that!) and Colt didn't want left out, but at the same time considered S&W and S&W cartridges to be beneath contempt. Still, customer demand could not be totally ignored, so Colt sort of "snuck" its .38 Special revolver onto the market by modifying the barrel and cylinder of its New Army and New Navy revolvers; AFAIK, they never advertised the new "feature" letting dealers and customers find out for themselves. Later, of course, that model was revamped internally and became the Army Special, the Officers Model, and the Official Police.