Yes, any item you store in a stash is safe, and you won’t lose any of the items after you put them in the stash. Given that you are building each stash crate and they look very camouflaged and inconspicuous whenever you examine the art, it’s safe to assume most people aren’t going to throw themselves at robbing your stashes. So you can store the emote loot items in there, even the higher-level ones, without any major worries about losing your items. Just be careful when going to get your items from these places, as some of your stashes can be placed in very dangerous areas and you might need to fight to get to them. Or at the very least you will need to be cautious.