After nearly giving up I cracked the code.
Solution
The only requirement for the game (full installation) to see DOSBox mounted CD-Image and, consequently, run is the presence of "OLD_HERC.DRV" file on it, which HAS TO have hidden attribute. That's it. My game now runs and plays on 64 KB sized ISO with only one 264 bytes file in it. How cute is that?
Note that the ISO has to be imgmounted via DOSBox exclusively. Mounting with virtual app and then mounting the drive with DOSBox wont work. You can add CUE and compressed audio tracks for in-game music and then imgmount the CUE for the complete experience at ~quarter of the size.
It's possible you will have to include some more files from the CD which hadn't transfered even during Full install (whole KEATING & LAUNCH folders, and few other files) into the aforementioned ISO just so the game doesn't crash if it needs to load data from them sometime later. I've no idea if that's necessary though. In my short test of loading the first mission everything ran without a hitch up to that point.
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It came to me late night yesterday when I focused on the DRV file because it precedes the no-CD error in MECH2.EXE hex view. Precisely, I had to add the file as 'normal' and the switch to 'hidden' before creating the ISO because my go-to app unintuitively disables hidden file handling by default. It simply refused to add if it had hidden attribute. Had I noticed sooner there would be no topic to begin with. So in the end it turned out that the MW2 CD-check isn't anything special after all - on the contrary in fact!
EDIT: Look like the exact same solutions has been posted HERE, a decade ago by noabody (good job Sir). Well isn't that cute, wish I'd seen it couple of days ago 😒