If you aren't familiar with the north peaks, be warned that it is nothing like the south peaks.
Although walking off paths can be done to get a direct route, it is very difficult terrain, heather bushes cover flat areas with deep peatbog gullies crossing the plateau's at random. These can easily be 8ft deep, with near vertical loose wet mud walls, so trying to find a route around or past them can be difficult, even in good weather.
Although this can be interesting/fun, I would personally choose to follow the pennine way to Dr's culvert, as this is a made path, then follow the snake pass down to the Inn.
That would give a route of over 20miles in day one however, and picking a nice route for the other days will likely end up a similar distance.
Not sure what distance you are used to, but I would rather cut down the distance or walk for more days and take a slower pace to enjoy it more.