Let's start off by pointing out that the primary weapon the Death Star uses is the Superlaser. And it is exactly that- a laser. Now lasers of this magnitude were typically composed of superheated, energy rich gas (which then turns to plasma).
Now the biggest thing about plasma, is it is able to be contained by magnetic fields. You can see two green "barriers" around the actual laser (which flashes from red to green). The individual temperatures of the 8 lasers are probably negligible pre-combination, and as you have magnetic shielding to ensure no plasma escapes, and air itself is a remarkable insulant.
However, the light emitted would still probably rate in the levels capable of damaging the human eye. Hence the helmets (as @valorum said). Outside of that, no harmful radiation (to humans) would be emitted, unless you are within the magnetic containment during the firing process. Regardless, nobody has complained about adverse side effects from standing inside the laser containment during activation yet!