Honestly it's much better to just not let predators around prey period
No matter how nice a cat may seem,accidents happen and those accidents can be fatal.Plus the prey drive of cats is never fully eliminated(they're obligate carnivores,with the nondomesticated relatives eating rodents in the wild including hamsters).I'd personally rather have torn carpet than a dead or seriously injured(or seriously ill eventually due to unnecessary stress)pet.
Even small cats and dogs can cause serious damage to tiny hamsters(munchkins for example would even be able to kill small rodents,as would chihuahuas and other small dog breeds).It may seem like a minor injury for humans when they get scratched or bitten by a dog or cat,but considering how delicate and small hamsters are it could lead to internal injury or lost limbs(among other things).Plus cats "interacting through glass" could be more curious for less nice reasons,and as for mourning it could very well be the stress of a change or even just feeding off the energy given by an owner.
Having prey animals and predator animals in the same house is entirely possible though,but only if the prey animals have a predator free area with secure doors.Some cats can open doors,so make sure they can either be locked or that you don't have door opening cats!