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I've never heard of whimzees or greenies impacting pouches, it usually soft mushy foods that cause pouch problems so I'd be more worried about them pouching something like their porridge than a bit of whimzee!
I don't really see it happening as they chew little bits off & I would imagine mostly swallow that as they chew rather than pouching it to hoard.
I've used Whimzees with all my hams & my Chinese have greenies very ocassionally which they prefer (probably because they're sweeter!).
Apple wood is fine but none of my hams have ever shown the remotest interest in chewing natural wood & hay tunnels you need to check over for any sharp bits that could damage pouches, I'd put them in the freezer before use too.