I clean Jacko's cage, sleep carrier and her playgym daily, I use newspaper---coloured and black-and-white. I don't know about where you live but I know the ink is non-toxic. Litter in my opinion is messy and expensive and if it biodegrades that easy you have to wonder about aspergillus spores n the like which you don't want your bird exposed to you if can help it. Especially if its sitting around for a few days.
As for it ripping, when you are changing the paper, fold up the ends and corners and roll it like a burrito---if you pick it up right almost nothing will come out. Then, bang whatever is left on the tray into the garbage can and give the tray a wipe down and you're good