That route is impossible with anything other than a full suss MTB. The road off Long Hill down by Fernilee is OK, I've done it on a road bike and it's just about passable. The left turn at the top of the Goyt (Macclesfield Old Road) is very rough as far as I can see. I've never ridden it and wouldn't want to try on a road bike. Maybe just about possible on your CX but not sure
The turn off the A5004 (Long Hill) back to Whaley is completely impossible. Stupidly I had a go on my road bike once to see what it was like. It was a nice walk I suppose
I've plotted a quick ride out of Whaley for you that takes in some little lanes that you're not planning on riding otherwise.
https://ridewithgps.com/routes/14447663
BTW, The Bike Factory in Whaley Bridge is where I take my bike. If you need any fettling, they're good