Do you have any evidence of individual pages having different rules than the book as a whole? It's a plot point in at least one episode (I think multiple) that individual pages ripped out can still be used (it's even the entire point of your hypothetical). Why do you believe you touching an individual page wouldn't let you see the Shinigami?
Why do you believe you touching an individual page wouldn’t let you see the Shinigami?
You can. But the thing with death notes, is that shinigamis only follows the owner of a death note, not people carrying a page. As far as I know, no shinigami ever followed Takada.