Hi. No cat litter isn't safe and it isn't good to spread any kind of granules under bedding either. The best way to resolve such issues is to have a good enough depth of bedding ideally and a litter tray with Chinchilla Bathing sand in it - must be sand, not dust (if your hamster will use a litter tray - Syrians almost always use a litter tray, dwarf hamsters can be less reliable!).
If you have 5 to 6" depth of substrate, then the bottom half usually stays clean and dry and you can just "spot clean" the pee areas a couple of times a week - or just empty the litter tray. Our Syrians have always used their potty/litter tray and the rest of the cage stays clean and dry
Then you just empty the potty a couple of times a week and replace the sand. The trick with the potty/litter tray, is to put it in the area they have chosen as a toilet - otherwise they ignore it and keep peeing in the same place.
Is it a Syrian or dwarf hamster? As regards drips from water bottles I get round this by having the water bottle over a shelf, with a small piece of granite under it (or a terracotta plant pot base). This does two things - soaks up any drips, which then evaporate, and also helps keep your hamsters nails trim so they don't get too long - as they walk on the rough surface every time they go for a drink. For this reason as well I use the small 75ml mouse sized water bottles, which are a good size for a hamster anyway, and their water needs changing every day or two anyway.
I use these, which come with a handy cage clip as well (and they don't really drip either which is another reason for getting them), which makes it easier to get the bottle in and out. Some people use the "classic" 75ml mouse bottles. You can use it without the clip of course if you have a tank - or velcro the clip to the tank.
https://www.portonaquapet.co.uk/shop...rinky-B-M42882
Shown in photos below. The hamster is our lovely Syrian, who went to the rainbow bridge recently, when he was a baby.
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