Always drop the Non Cluster Index first as it has reference to Cluster Index.
If Cluster Index was removed first, non Cluster Index would have to be updated on cluster index removal.
When you build index, first build the Cluster Index and then Non Cluster.
Note: All NON Cluster Indices can be build simultaneously once Cluster Index is created.
During Index Rebuild, one of the parameters a user can set is Statistics_NoRecompute.
The default value is OFF which means "Automatic statistics updating are enabled"
ON = Out-of-date statistics are not automatically recomputed