Yup. Take the second shortcut and run past all the monsters. Using both grace and athleticism helps, too. Now which chests are we talking about? The ones that Daimon guards over, or the ones you encounter on your way to him?
The ones made available to you after you kill him respawn immediately after exiting the Bitterblack Sanctum through the spiral stairwell, and the ones you run by on your way to him would take a couple of days of sleeping to respawn.
Xbox GT: The Crusader 39 Level 200 Mitigator/Pioneer fighter pawn. Friend requests are welcome. :)