The shield granted by Wooden Cross takes priority over the Holy Mantle's shield and can allow two nullified hits of damage upon first entering a floor when paired with Holy Mantle.
Bosses are generally more difficult than regular rooms, meaning that it is often wise, especially when playing as The Lost, to immediately drop the Wooden Cross at the start of new floors, then clear rooms until the Boss Room can be entered, and finally backtrack to pick up and use the Wooden Cross.