Agree with Luna - better to use the grass hammocks or rat sputniks. Apart from chewing fabric there can be other issues with hammocks and hanging toys such as feet getting caught in eyelets or chains. You can get round these issues. I have only used a particular brand of fleece hammock (very well stitched) with very old hamsters who are past chewing stuff
Anything fabric is risky for chewing. A ball of sisal string can be useful for hanging or tying things to bars - that is safe to chew.
Instead of a hammock I have a rat sized tube tied to the roof - leading to a hanging rat sputnik. They like those because they're round and it's also something to sit under - they like things overhead to sit under. The rat sputniks work best with some bedding or hemp mat inside so they're a bit cosier.
Love your Alaska set up Ria.
This is a pic of the roof tube and sputniks in my cage - which is about the same height as the Alaska.
Attachment 51042
Attachment 51043