Yes, Steve, there's a path that's been created that covers nearly all of the link you're after. We've used it 2 or 3 times in the last year. It's on the RHS as you head up towards Llanberis Pass. It starts just out of Nant Peris and mostly it keeps a stone wall between the road and you.
Unfortunately it stops, probably 300 or 400m (from memory) before the footpath you're heading for, and there's no alternative but to keep in and go single file by the wall until you reach the lane entrance to the footpath you want on the opposite side.
As I said, we've done this a few times - with kids you'll need to impress on them the need to keep in and pay attention, but the traffic we've encountered has always been ok, not travelling overly fast on account of the bends and the proximity of stone walls to paintwork!
I've never spotted any alternative - the land in the valley between the road and the river on that stretch is pasture divided into fields and typically being grazed, so there's no open access.
Btw, that footpath up into Cwm Cneifio is an excellent route, especially the first half, very quiet in comparison with most of the Glyders approaches, and some fantastic views across the pass to Snowdon and Crib Goch.
