If you're that concerned, you'll just have to rig two ropes industry-style and use a professional fall-arrester on the backup rope, like an ASAP or similar, which requires no hands to operate, unlike a Shunt or a Duck. It's a pain, but that's the only serious way of doing what you want, if you're descending solo. That said, you'll still be hanging in your harness for a long time until the rescue comes if your backup kicks in and you're unable to start climbing to unload it - and depending where you are in a system, that could be as serious as a fall that injures you.
That said, if your main rope fails, it's either the anchors that were suspect or the rope's rigged to rub on a sharp edge, neither of which are acceptable practice, even in groups. In which case, whatever your backup rope is attached to needs to be more reliable than the original anchor or that'll also fail under a shock load, rendering the fall-arrester useless anyway. In which case the original rope should have been rigged from the more reliable anchor too! There's usually only one set of (usually reliable) anchors on most cave pitches. Wouldn't it be less stressful (and cheaper/lighter) to go caving with someone else if doing SRT?
