Escaping a world as Woodlegs and choosing another Character, will not despawn any Lucky Hats in the inventory, letting Characters other than Woodlegs, use them.
Doing the same thing with Warly, will properly despawn his Portable Crock Pot but won't do so with the Pouch. That said, if unequipped the Pouch will be invisible and can only be interacted with by pressing the spacebar. If choosing Warly as the PC after changing worlds with another Character, will not give him is Portable Crock Pot at the start of the game, making it unavailable to him for the rest of the game.
Walani and Woodlegs don't get a free Surfboard, Lucky Hat and Sea Legs either when choosing them.
Wickerbottom's Joy of Volcanology Book, unlike the other Books, does not decrease any Sanity. Also an Ice Flingomatic will not act as Ice when extinguishing the Lava Pools formed from it, dropping Rocks etc. instead of Obsidian.
Hop worlds with Walani, Warly and Woodlegs and observe how their items stay/don't spawn in the inventory. Use Wickerbottoms Joy of Volcanology book near an Ice Flingomatic.