Hi! By bedding I'm guessing that's the stuff covering the base of the cage? Kaytee Clean n Cozy is a really good bedding option yes
Hamsters do have a faint 'hamster' scent, and male hamsters cages will smell a bit more because they tend to pee a bit more around their cage. But they shouldn't smell that strong...
Just wondering, have you tried giving your hammy some sand in a box or Tupperware tub? Hamsters love digging and washing themselves in bathing sand, and this kight encourage your hamster to wash a bit more carefully if that ends up being the issue...! I use Tiny Friends Farm bathing sand in a couple of rectangular Tupperware tubs in my Syrian Maisie's cage (she uses one as a potty, hence two tubs not one!). She loves washing and digging and playing in them