You do not have to walk up the centre of the Nick unless you want to. There is a route from Murton the circles the Nick. If you do go up the middle, then, as you surmise, it is a steep rocky climb out of it - the only real exit is through a cleft at the very head of the Nick. Be prepared to duck, I once saw an RAF Tornado fly down the valley - his timing was good, he missed the light aircraft going the other way by a good 3 minutes.
If you take in Murton Pike, look out for the misogynistic buzzard as you head down the saddle (if it is still there).
Edit to add: Ignore the line of the PROW up the middle of the Nick - it is a work of fiction. There is path though, but not much of one. Also the FP out of Keisley Bridge is much the same. Enter or leave via Habour Flat and use the farm track. If you elect to go round then I have a trace on the OS app.
Some indication of line can be had by tying these two together
https://osmaps.ordnancesurvey.co.uk/route/315373/130929-Highcup-Nickhttps://osmaps.ordnancesurvey.co.uk/route/1911484/150709-Warcop-RangeSorry I don't have a trace for up the middle