Note: I posted this answer yesterday but deleted it because I didn't think I'd understood your question properly. But given the additional info you've posted, I actually think it may be what you're looking for. (if it isn't what you're looking for, please let me know and I'll delete it again)
Something like this:
This is some <span style='display:inline-block; width:0px; overflow:hidden; white-space:nowrap;'>copy me!</span>random text.
This is some random text. on the browser, but when copied and pasted into Notepad, it should give you
This is some copy me!random text.