When hamsters chew sticks you sometimes can see little teeth marks. Check to see if there are any. If not, it isn't very surprising. Most hamsters refuse to chew wood. Mine likes loofa, but yes, this is usually when I would throw in some Whimzees. Or Greenies. Probably Whimzees.
Here's a Whimzees v. Greenies thread, in case you have some difficulty deciding which dog chew to buy:
Greenies or Whimzees?
Some people say Milk Bones are ok too, but the ingredients are pretty horrid, so I didn't get any.
EDIT:just noticed you already said you didn't notice any teeth marks. Ignore the first 2 sentences, please.