@fountainbridge - you want a pavement? If so then Harlaw road fails as it has a short section of couple of hundred yards after the last house before the layby corner where there is a path again that avoids the road? I did this with small children buggy, buggy board etc for several years. Through malleny estate behind the high school. You don't want a pavement? Through malleny, couple of fields then out to where the underground water tank is on Harlaw road also with sloping lAyby and you are beyond the pavement.
Or you want to do it avoiding road but don't mind a scramble? There is a path parallel to the perimeter road in Balerno (crosswood) that follows a burn and winds all the way up past the water treatment works onto the Rigg road at thriepmuir but you do have to cross roads in Balerno
100% no pavement - Currie (walk WoL path to Currie) take The poets Glen from the WoL path. Poets Glen is all off road to the farm maybe Easter bavelaw. Go through the farm and you are on torphin hill. Go round the farm cottages and you are on a track that goes round to Bonaly. FAirly sure this is compliant with being all off road. the poet's Glen is quite passable, some of the old bridges have rotted and have spars of wood missing. Not great for buggy or wheelchair but fine for the ambulant.