Are you keeping them in the same cage? Please do not if you are. And if you aren't, I doubt it could possibly get sick if you washed your hands after holding and snuggling him, etc.
No of course not, i dont even have it yet i know that mixing species isnt a good idea. Do you think putting the hamster cage on top of the pigs cage would disturb them?
Yes, but sometimes a species can pass diseases not harmful to them to other species that can be harmed by it. If guinea pigs and rabbits live together, the rabbit may pass on Pasturella Bacteria to the guinea pig, which is unharmful to rabbits, but deadly to guinea pigs.