Shaco can move around his clone be recasting his ult. So does this mean that you can not move you clone when you are silenced? Since you cannot cast or recast while. silenced
And does the same go for a like ults(Annie comes to mind)?
Honestly I've never moved Annie's bear or Shaco's clone by recasting their ults, so I can't speak for that part of the question.
Before they added the ability to recast the ult to control pets, the only way to do this was by using the alt key.
If you right click while holding down alt, it gives move/attack commands to "pets" like Tibbers or the Shaco clone, rather than your champion. I can confirm that this method of control is not affected by silence.
It follows that the ult recasting method should not be as well. If this isn't the case, it needs to be reported as a bug.