That would be a tough day. Think I would go Kendal-Bowness via crook, chain ferry across Windermere, hawkshead, Langdale, red bank over to Grasmere, over Dunmail raise then west side of thirlmere, St. John’s in vale to a66, cross to Threlkeld then scales, Mungrisdale, Caldbeck then north to Carlisle. Alternative to first bit would be to head over kirkstone to patterdale, then up over matterdale to trout beck, then continue as above to Mungrisdale.
Haven’t mapped these for distance but avoids wry nose and hardknott and a big Western detour. Another option would be to head east out of Kendal towards sedbergh then follow lanes north to Penrith on the east side of M6, probably a more direct way to your finish point at Brampton.
Edit: just mapped the first option on Bing and it came out at 68 miles, as far as Carlisle.