If you don't like the sound of them chewing, IMO, chinchillas are not the pet for you. They are rodents, they have continuously growing teeth and NEED things to chew on to wear them down. Wood is the #1 thing they chew on. Nothing else is going to wear their teeth down as good as wood.
I've seen other things used for shelves, sure, like solid metal shelves, or even wire mesh (small mesh, think 1/4" x 1/4" openings), but in the end, you still will need something for them to chew on... which will likely be wood.
If you don't like that sound... well.... you'll either need to get used to it or get a pet that doesn't quite chew that much, because believe me they chew. If they don't have access to things to chew on, their teeth can grow too long, and that causes a whole 'nother host of health problems.
The only other thing I can really think of that chins chew on, other than wood, are pumice, loofah, and cardboard. Personally, I think the cardboard is louder than the wood. But everything else I keep thinking of to type here is wood. They're chins, they chew wood. That's just how they are....