Not sure, but to hazard a guess, could be a railway dispatch cancel. (And of course, not
strictly a CDS because it's a squared circle

)
Edit: You edited in the second image while I was replying. Even less sure about that one, but I'd still guess railway dispatch, if pressed.
Do you have an equivalent IN CDS on a stamp? I'd assume IN ought to appear only as a backstamp, if my guess is correct.