I used to have (or maybe I still have somewhere?) something similar but relying not on a VM running on host but booting from USB. I’m not sure which assumption is more realistic, that you will be able to access boot menu or that there will be particular brand of virtualization available on the system you’ll be running on

EDIT: I think there also was a distribution with something like this in mind. Like the image of OS was compressed, after GRUB it was decompressed to RAM from which it was really running and there was some way to “updated” the image on USB