Alpha emitters are completely harmless at a range of roughly 12 inches and are blocked completely by light shielding such as a piece of paper or a bulimic supermodel.
Close, but they're actually blocked by skin and are pretty much harmless as long as you don't eat or inhale them.
As for the question of whether nuclear power is safe, the more sensible question to ask is how safe it is relative to other forms of power. Not counting Chernobyl, there have been a grand total of 10 deaths from civilian nuclear power*. Chernobyl caused 53 directly, and probably on the order of 4000 over time, but is hard to get an exact number.
In comparison, according to official figures there were 4749 deaths in coal mines in China just in 2006. In a single country in a single year, coal power caused more deaths than nuclear power has in its entire existence, before the coal even managed to get out of the ground let alone into a power plant. Throw in all the other direct deaths, then add things like acid rain, oil spills, global warming, and so on, and any comparison between nuclear and fossil fuels is just laughable.
Of course, this doesn't mean nuclear power is perfectly safe and that we shouldn't try to make it even safer. This accident is particularly sad since modern designs can't fail in the same way. Hopefully soon we'll get accelerator driven sub-critical reactors working which are as fail-safe as it's possible to get. But even without that, it just makes no sense to start crying about how terrible nuclear power is because of a single accident that's only killed a single person. Where were all the cries to shut down coal plants when 29 people died in New Zealand a few months back?
*Edit - for clarification, these numbers were from Wiki and I haven't checked to make sure it's all inclusive so the actual number could be a bit higher. It's certainly only low double figures though, so the point stands even if I missed a few.