Sounds unpleasant in theory, but it works! I don't know what kind of wood the shavings are from, but they're sold in big bales as horse bedding so some kind of softwood I'd assume. It works much better than the grit - absorbs odour at least as well, doesn't get stuck to their paws, and of course it's biodegradable. But what we're doing so far is piling it into the bin and sending it off to landfill, as we're not too comfortable with having a pile of cat waste down the bottom of the garden. Can anyone suggest a way around this? Bin collection here costs 9.50 a pop, ouch!
(I know there are some people who say that a cat should be either permanently indoors or outdoors, and not both at the same time, but there are some fairly dangerous animals around here that a kitten could neither fight or run from, so we keep them in at night.)
The simplest ideas are always the best it seems! A cat version of that digester might be worth a go, although it might work a bit differently when there's a load of wood shavings and urine included. There's an experiment worth taking on.
I use it to deter critters like mice, rats and rabbits by spreading it around the perimeter of our yard. If I get holes from mice, I dig them up, load in a bit of used catlitter, and the diggers are gone for a few weeks. I use a woodbased litter, so it's basically the same as shavings.
My cats are mostly indoorsy galls, hunting in our garage where I store hay, straw and feed for chicks and rabbits. They are healthy and parasitefree. While I don't spread their litter around veggies, I don't really worry about healthrisks.
If your climate has enough of a warm season, you could sift out the turds and give them to black soldier flies. These will produce poultry or fish food and the residue will readily compost. Same with dog and humanure, too. Any compost system up to standards for humanure should be able to handle dog and cat as well. If nothing else bury in holes around your trees and shrubs. Don't let nutrients or organic matter off your land if you can help it. Having sifted out the poop, you could age the wood shavings and re-dry them and use them again. I find the deodorizing factor of half-composted wood chips or shavings to be superior to fresh ones, and the addition of a bit of ashes helps even more.....
My cat litter is basically sawdust too- and I also have 'outdoor' cats kept in at night (it limits the number of 'presents' I get in the morning). Compost it! Mine goes into an insulated composter (which is a wheelie bin with some polystyrene insulation around it) which maintains at least 40C year round. Completed compost used on the garden- which includes both flowers and veggies.