We started from Threlkeld a couple of weeks ago and added an up and down to Skiddaw House and a cheeky down Doups.
According to Garmin, from the start of the car park & BW at Whit Beck to the Hotel at Ravenstone it took us 1hr 53mins, but we don’t hang about. We had a good pace on for the hikeabike, stopped at the summit just to put jackets on and then rode from the the trig point and did all the Pike in one hit (apart from one section that’s washed away where we couldn’t find a line this time).
I reckon there’s a quicker, easier and more rideable route up Skiddaw from Skiddaw House via Sale How but what you’re planning is still the quickest IMO.
Enjoy.