I would just have it generate and then put it side by side with a blank document and type by hand, and edit as I see fit without copy-pasting the text.
That's not how watermark works for ChatGPT. The watermark is the sequence of words. It has nothing to do with the string representation (e.g., invisible characters or whatever). Even if you modify the sequence of words slightly, the watermark is still recognizable. You would have to modify the sequence extensively, but then it would be like writing the thing on your own... so there would be no point on using ChatGPT.
What's your source on this? The watermarking that you're talking about sounds highly speculative. While it may be possible to encode an identifier in a long enough string, I don't think the average (relevent) ChatGPT output has enough entropy to meaningfully identify it from billions of other potential outputs.