I realize that designers and printers have for years repurposed existing CMYK files for different projects, even on different presses and papers. A skilled press operator can even make it look pretty good.
But a CMYK file is, if done properly, very specific to a size, sharpening, press, and paper. In my mind it's a one-off file in the same way that a tiny web-size jpeg is a one-off. It shouldn't be re-used.
So for me, I would generate a new CMYK file from the original raw for each new project. That's semi-easy with Lightroom, as I can easily find the original raw file, but then of course LR won't directly create CMYK, so I need to export a 16 bit TIFF to Photoshop and make my conversion there.
I have managed to get our staff designers on the same page in the last few years, so we're working from originals and outputting new images for new projects.