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Fleece is the fabric used most often for things like hammocks etc, you do need to keep a careful eye on them for chewing but if they don't then it's ok.
Plywood may not be safe due to the glues used in manufacturing it, kiln dried pine is generally the safest wood to use.
Bear in mind that if you have a wooden cage you will need to give it at least two or three coats of Plastikote water based enamel to completely pee proof it & make sure there is nowhere your ham could get his teeth in & start chewing!
melamine board is safe as long as your ham can't get to the edges & chew & is also waterproof so overcomes the pee problem.