If it helps, switching from the regular map layout to the "
National Park pathways" view on the OS Maps website does show a path - whether this translates to an obvious path on the ground is another matter.
I've used this feature a lot when plotting routes and it's mostly worked out okay - it picks up a clear and very walkable path along the side of Alport Dale, for example, that doesn't show on the normal map layout; on the other hand I once tried to follow one of these routes from the Wain Stones to the top of Torside Clough on the north side of Bleaklow and there was no indication on the ground that anyone had ever traversed these groughs and hags before me (fortunately, it was pretty dry underfoot!).
The marker I've added on the above map is Shelf Benches.
If you do venture up that way I'd be interested to hear if there is a semblance of a path at all, as I have a plotted walk that heads up onto Bleaklow via the same route and then south to Crooked Clough. It'd be handy to know whether I need to pack a snorkel!