I would never trust any of those machine, even if they claim they don’t track what has been stamped.
So, either we buy one of those for personal use, and then we are ready to destroy it after the first use, or the washer method is superior in security terms.
Based on the laser CNC idea from the Italian board, as seen below, how about using an actual (cheap, DIY type) CNC router?
From what I can tell, you can get DIY CNC routers for $200-$300; compared to laser etching, you can't hurt your eyesight, the cut would be deeper and it should be much quicker (though a bit messier).
What's nice about these simple machines is that in general (from my experience with 3D printers), they don't save the code persistently. When they're turned off, they essentially 'forget everything' and often print / cut from a microSD card directly, which you can wipe after you are done. It can also be generated offline with the supplied software or something more elaborate on a dedicated laptop. Most people who do 3D printing and milling have a dedicated machine in the shop just for the purpose of generating toolpaths anyway.