Whether you are packing these items yourself, or you are asking the movers to do so, it is possible to save time on the process. If you are taking both the items and the furniture that contains these items, you do not have to take the items out of your drawers.
Ask the movers to take out each drawer individually, and then wrap it up with bubble wrap or plastic. That not only protects the drawer, but also ensures all items will stay inside. It saves a lot of time while packing and unpacking.