* The character who disguises himself as David is Magua. Magua, a Huron warrior, takes on the identity of David Gamut, the singing schoolmaster, to deceive the English soldiers and gain access to Fort William Henry.
* Hawkeye is not involved in the plan to escape. While he does play a crucial role in rescuing Cora and Alice from the clutches of Magua, he does not disguise himself as David to do so. Hawkeye's main tactic is to use his knowledge of the wilderness and his marksmanship to outsmart Magua and his Huron allies.
Therefore, the premise of your question is incorrect.