Might be wasting my time but.....
Possible itinery, approx mileage starting from Hessle would be..
Day 1, 23 miles to Goodmanham (Manor Farm £10)
Day 2, 14 miles to Huggate (Wolds Inn), free to camp as long as you eat/drink there.
Day 3, 18 miles to Wintringham (Yorkshire Wolds Way Caravan & Camping £12
Day 4, 23 miles to Filey (Filey Brig campsite right at the end, from £8