Once you go down mount vic theres a turn off at hartley for cox river. You can follow that road and it eventually ends up in jenolan state forest. You can work your way through the forest and come out on jenolan rd.
Looking at Tracks4Aus there is a track about 2-3 kms west of Katoomba along the highway (looks like it is called Nellies Glen ) which heads down to Euroka which then crosses the Cox's River and heads to Black Range which then takes you to the Jenolan Caves Rd.
Doable ? no idea but it is on the map.