One of the parents can stop by the self storage facility on the way home from shopping to drop the presents off in the storage unit so that the bags do not attract attention when they come home. In addition, keeping the storage unit stocked with rolls of various types of wrapping paper as well as tape and other things that are needed to wrap the presents will make it even easier for the parents to keep the presents a secret. A small folding table and chair can make a perfect wrapping station because when they are collapsed they do not take up a lot of space.
If the parents have purchased one or more presents that need to be assembled, they can do this in the privacy of the self storage unit. This gives them ample uninterrupted time to complete the assembly process without the concern that they will be discovered midway through the process. They can also test out any presents to be sure that everything is working properly before giving it to their children. In addition, the parents can take off all of the security straps, tape, and wires so that the children will be able to play with their presents right away after unwrapping them.