Load up the chests to be picked into another chest or container and the use the "I wish to lock this down" command instead of the "I wish to secure this" command. The "I wish to lock this down" command will lock down the main chest and will also automatically lock down every item inside the main chest (sub-chests and keyring with keys) so that a player can open the main chest to pick locks inside, but they can not remove any items.
I "think" that is it. Hopefully someone here can confirm, or you can test the results with a friend.
Safe Journeys!