It seems I spent so long typing my last post that I missed the leader's map.
If you follow the blue line it will take you under the A8 to Gateway and then up a ramp to the cycle path along the A8.
The cyclestreets route looks good as far as the Gyle but may not be entirely surfaced. I would cross SG Broadway at the tram stop and then head for the underpass either through the car park or round the edge of the Gyle. There is some unpleasant road crossings on the marked route.
The path to (and across) Renwicks appears on the map but it correctly wont route you over it. The track is rough and over overgrown but an oasis of quiet in the area.