I would wonder what might happen to cat litter if it got damp, and some types do give off dust.
First one done with :meow:litter, I did poke a plastic bag in to line the doorstop and just trickled the litter in. I did it to stop the dust, hadn't thought of the damp, but there you go. I don't suppose it would be any more affected by damp than rice etc, and won't be susceptible to weevils and other bugs either.
This being the prototype, and me being myself, I thought of a few improvements overnight. I used a freezer bag, but think I'll double line the next one, to be sure to be sure.
If it's not successful then it's no great loss, an afternoon's hiding in the sewing room, the ends of a curtain I shortened and a bag of Aldi's cheapest :meow:litter.