I used 2.1″ Maxxis Crossmarks (70a) @ 40/60psi f/r on my XC hardtail in anticipation of some offroady bits. While they were fine on the roads (keeping the rear nice and hard), aside from climbing the old coach road and dropping to 40psi (was nearing the campsite anyway) I didn’t really have any need for tyres ‘so’ chunky
The climb out of rookhope ought to be doable on slicks and some smooth pedalling
(Granted I missed out some of the offroad bits round nenthead/allenheads and the big climb beyond penrith due to time/others in group)
Since doing so I’ve ridden the pennine section of the transpennine trail (from manchester to nr. doncaster). I thought it’d be similar in railway paths with less offroad so I opted for my rigid bike shod with nigh on slick continental sport contacts (1.6″). I also reccomended a friend get some slicks rather than keep with his knobblies (he asked whether he should), and another use a trek 1000 road bike (slicked up as I’d ridden with someone on the C2C on a flat barred road bike do all but the non railway path offroad stuff)
Turns out in march much of the railway paths are sloppy and there are some rocky bit over the top of the pennines
Apart from another (non MTBer) friend on slightly treaded slicks and another on knobblies (who destroyed himself even with very high tyre pressures), we had a great time. The sloppy bits were suprisingly rideable even with 80psi slicks, fast going and fun, reasonable on the rocky bits (very fast on the tiny bit of down) too (not so much the tiny bit of wet grass over the tops).
Anyhow, with a bit of MTBing skill and some smooth pedalling nigh on smooth slicks will do you fine IMO