I can tell you from experience that if you wear glasses that use plastic lenses you're probably going to be fine. Let me explain. I was modding my PC with some CCFL blacklights, basically the same UV range as the LEDs you've got there. I had just gotten them and was testing them out in the kitchen which, due to an awning, was typically pretty dim as it was that afternoon. Anyways, the CCFLs are really thin and were supposed to be used inside an acrylic (plexiglas) tube for their protection. So anyways, I fired them up and was really disappointed with the output. I could see them, but they hardly made anything glow, even nearby. For whatever reason, I slid one out of the plastic tube and it was a whole different ballgame. Imagine the chorus of angels singing Aaaahhh! when I did. Suddenly stuff several feet away started glowing in the blacklight.
So, yeah, apparently acrylic and probably polycarbonate is not very transparent to UV light. If nothing else, wear a pair of safety goggles if you're worried about it. As long as you're not shining it right into your eye, the scattered light shouldn't be an issue. It's almost certainly going to be less than what your typical fluorescent blacklight gives off anyways and people have been spending hours a day staring at stuff illuminated by those while smoking weed for decades now and still haven't gone blind from it.