Some random containers are safe, some aren't. Certain container types (distinguished by the readable name when looking at the container) are set to never respawn, regardless of their location. The Elder Scrolls Pages has an article on these Safe Containers.
That page has additional details and pictures of each container. They include:
- Child's Chest
- Noble Coffin
- Burial Coffin
- Common Cupboard
- Upper-Class Cupboard
- Noble Cupboard
- Common Dresser
- Upper-Class Dresser
- Orc Dresser
- Common End Table
- Upper-Class End Table
- Noble End Table
- Orc End Table
- Riekling Hut
- Sack (not Large Sack or Small Sack)
- Strongbox (not Strong Box)
- Noble Wardrobe
There are also Safe Locations that never respawn, meaning that none of the containers in the location will respawn, regardless of their type. This includes player houses, as well as many other locations.
However, none of this matters for your immediate problem.
Delphine will take all the stuff you didn't give to Malborn before you go inside, and give it back to you after you're done. As stated on the Elder Scrolls Wiki:
There is only one chance to give him [Malborn] gear. Nothing else can be given to him once the trade dialogue closes, and remember nothing else can be taken inside; give it to Malborn. Give him some lockpicks, since there will be locks to pick.or just favor your items and you can still equip them even if there not in your inventory.
Afterwards, the Dragonborn will meet with Delphine at the Solitude Stables at Katla's Farm to pick up the invitation and party disguise, and then drop off everything else on hand with Delphine; everything given to her will be stored safely until reclaimed after the mission. Delphine will store the inventory in a chest in her hidden office in the Sleeping Giant Inn, in Riverwood.