Maybe. Personally, I would want to see A LOT of math and paperwork first before I listen to anyone who uses "perfectly safe" and "nuclear explosion" in the same sentence. I'm still hoping we can figure out some other form of space travel which doesn't involve really, really, really big explosions.
Micro craft with light sails propelled by lasers have been discussed quite a bit. My favourite instance of it is in Charlie Stross's novel Accelerando.
I would guess that radioactive particles on the surface would be different that radioactive bombardment from space. You could shield your shelter from space, but if the soil had radioactive particles in it, then you couldn’t bring it in your shelter. For that matter, you would also have to shield the floor, or at least remove a layer of soil. You might have to do that anyway to build a foundation.
If it isn’t obvious, I don’t know what I am talking about.