I didn't answer the question, because it didn't seem relevant, as the real point was about the usefulness, or not, of carrying a POH on board an aeroplane.
I hand swung an aeroplane with a flat battery on Friday. It wasn't a C172, I did have somebody I trusted and had briefed strapped into it.
I try to avoid C172s for several reasons, the main one being that I'm a shortarse and can't see over the instrument panel on most variants. I might avoid hand-swinging one mostly to give me an excuse to fly something nicer, or because I don't have gloves to hand, or because I haven't established that there isn't something more serious wrong with it than a flat battery. Mostly to have an excuse not to fly one.
G