I've thought about this a lot, and the best I came up with is a wee bit round-the-houses, but quiet:
http://www.mappedometer.com/?maproute=632200
Go from Kingsknowe Road North through Redhall and drop down to the signalised junction at the new Sainsbury's by the viaduct. That makes the right turn easiest. Then a bit more bus lane takes you to the WoL visitor centre, and the path to Gorgie. Cross using the crossing point and carry on along the path to Ford's Road and Stenhouse Avenue.
Stenhouse Avenue is quiet, and you use that to get to across the tram route to Carrick Knowe Avenue. Pinkhill comes out on the A8, and then SWMBO can use the bus lane (which is also pretty quiet) to get to the ped crossing at the zoo. The Pinkhill option is a more legal version of coming out at the Forestry Commission building and riding along the footway to the same ped crossing at the zoo.
Works out at a bit over 4 miles and no steps or sharp gradients. Maybe the odd kerb to bump down at Ford's Road if they haven't fixed it yet. I would avoid the Calder Road underpasses, personally, partly because of the blind corners and partly because they're just so much faff to use.
To get from the WoL path at (say) Juniper Green to the Lanark Road/Kingsknowe, the probably easiest route is this:
http://www.mappedometer.com/?maproute=632201
in which you take the ramp at Gillespie Road, and cut through to Spylaw. The right turn from Spylaw Bank Road onto the main road isn't too bad. The little path from Hailes Gardens called The Turlies looks good on paper but there are chicane gates at the southern end so pretty much a non-starter.
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