sounds like a waste of time and resources. You'll still need a spacecraft to get to the rock, and there's the added trick of leaving it at the proper trajectory. Also, the ship will still need to be shielded, so if it's safe enough to be in space at all, shouldn't it be good for the whole trip?
As a side note, what are the radiation levels on Mir? Wait, it burned up didn't it? Don't suppose anyone has the readings on that before it reentered?