I think you are correct. I did a quick Google search for "K40 laser power supply pinouts" and found this which seems to match your picture:http://www.everythinglasers.com/wp-content/sp-resources/forum-image-uploads/scottmarshall/2016/11/WhitePSU-pinout.JPG
You should be able to do what I'm doing with mine and series the push-button for a "manual enable", the case lid safety switch, and a water flow and temperature switch (relay) in the water chiller. Just daisychain them all together from one to the next. All should be normally-closed to operate. That way if anything fails or a connection comes loose, it will shut it down.
From what I've seen online, your supply is one of the less common power supplies, but there's also lots of variations even in the ones that otherwise appear identical. If you've ever seen any of the pictures online of the early early versions of the K40 laser, they've come a long way. The early ones looked more like a kid's school science project. If you want a good laugh, do some Google searches for some of the old pictures of them.
Mine matches the one in the first link I sent, and it too has such a "test" button, but seems they've corrected the spelling by that iteration. Mine is about a year old -- still just now getting around to rebuilding it with a RAMPS board and such...