I would suggest a thin piece of card or paper, with a letter (or colour etc.) underneath. And put it under a casualty figure (or shell crater as above) when needed. So the opponent would not be able to recognize details of the figure (or crater) as permanently associated with a peculiar information.
…If there is no off table account at all, however, I don’t see how you would prevent someone to cheat and lessen the damage (but that’s another problem).
If you want to have a status marker with hidden information, simply write something on the underside. If the hidden information should be hidden to both players (i.e. neither players know the exact status), you could as well generate it when you need it.
Yes that’s another solution …and that would answer both questions. The exact damage would be unknown to all, till you need it and it is revealed. A kind of Schrödinger’s damaged unit…