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I think it depends on the individual ham as much as the species though Chineseys do seem to be the least likely to chew & love their cosy hideouts the most!
With any ham it's best to try them with things like that out of the cage first & if they seem ok it may be worth a try but they still need watching for a while to be sure.
I have used a snoozecube with a Russian ham too with no problem but one of my other Russians always had to attack anything new before she'd accept it so I never took the chance with her!