It's better to touch something once.
If you must touch it twice, use the second time as an inspection step.
Pull and Pack one order at a time, from packing slip to packed box.
Better: (2x with inspection)
Pull orders once, then pack them while double-checking the packing slip to ensure there are no errors.
Okay: (2x, no inspection)
Pull and pack an order, label with order #, then later label with shipping label. No opportunity to inspect the order for errors in the second step.