The radiation includes pretty much everything: For instance, the brightest radio source in the sky isn’t the Sun, but rather the black hole at the center of our Galaxy (called Sag A[sup]*[/sup]). There’s visible light, too, but nobody pays that as much attention, since there are plenty of visible light sources in the Universe (like, say, stars), so they don’t stand out as much in those wavelengths.
And Hawking radiation does exist (we’re about as certain of that as we are of anything about black holes), but it’s very, very faint. Black holes, unsurprisingly, emit as perfect blackbodies, and a typical black hole (i.e., one of stellar mass or larger) has a temperature of about a millionth of a Kelvin or less, far colder (and hence darker) than just about anything else in the Universe. We might conceivably detect the Hawking radiation from a primordial black hole (which can presumably be much smaller and therefore much hotter than the stellar ones), but from a normal-sized one, not a chance.