Space usually stops being dangerous once you get into some atmosphere. Nuclear waste doesn't.
Space is very irradiated, and direct sunlight is radiation itself. Anything you add there will be a drop in the ocean. Atmosphere is not sufficient to resolve space radiation, you need a magnetosphere.
You don't take sunlight inside with you when you enter some place.
You take neutron radiation (well, its consequences), but that is pretty much non-existent when compared to nuclear waste.