I see there is no such character, which I pretty much expected after Google didn't help.
The original problem I had was solved long ago but the recent article about watermarking reminded me of it, and my question was mostly out of curiosity. The task wasn't, strictly speaking, about "padding", but about marking - injecting "flag" characters at arbitrary points in a string without affecting the resulting visible text. I think we ended up using ESC, which is a dumb choice in retrospect, though the whole approach was a bit of a hack anyway and the process it was for isn't being used anymore.

