You can do the full db backup ahead of time. You can do a differential just before you do the index changes.

Script out all existing non-clustered indexes ahead of time also. Drop all n-c indexes before dropping the PK. Then create the clustered index. Then recreate all n-c indexes, including the PK.

The index sequence is always: drop n-c first, then clus; create clus first, then n-c.