If you get one of those jars and toilet train your hamster he should pee in his toilet but about poo they just go whenever and wherever
I personally spot clean every 3 -4 days winter time and 2 days summer time. Full cage clean is every month even then I'll leave plenty of old bedding and nesting materials as I don't want to stress my hamster out.
I'd say hamster poo and pee is pretty safe as so far I and my family members had no problems
I even let my hamster run on my kitchen work top while having morning coffee (well supervised from both sides!!!)
I'd say your hamster will not throw out his dirty bedding but he sure will chuck out his poo
they are very good throwing away their poo but their pee is more of problem as could lead to bacteria and fungal infection maybe ?!
