I think it's very clear that a Bunshin can't pull of that jutsu.
When Naruto created Rasengan he measured how much power he had infused in it, by the intensity of the pain (something like that).
If even the normal Rasengan hurts the body while creating it, that pain must be even higher for the shuriken.
Maybe the pain alone would destroy the Bunshin.
I just provided a possible explaination. Not that we really need one.
If a Bunshin could do it, nobody would've said to Naruto not to use Rasen-Shuriken anymore.
They would've told him not to use it himself and to let a bunshin do it.
If that were possible Kakshi and Tsunade would be smart enough to figure it out, don't you think.
For me that's enough prove that a Bunshin can't do it.
"For Feanor was made the mightiest in all parts of body and mind, in valour, in endurance, in beauty, in understanding, in skill, in strength and subtlety alike, of all the Children of Illuvatar, and a bright flame was in him"
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