Dusty Hammer
The Dusty Hammer (found only in Paper Mario) is an item used to damage one enemy for 1 HP. This makes it similar to a weak version of the badge Hammer Throw. It is one of the two items Mario must buy at Little Mouser's Shop in Dry Dry Outpost to see Moustafa (the other being Dried Shroom).
Aside from being needed to see Moustafa, the only other useful thing you can do with a Duty hammer is throw it at a Swooper, if you don't have the badge (or BP) to use Hammer Throw this early in the game. Without some sort of badge or item, it is not possible to attack a swooper while it is hanging onto the celling, as Mario does not yet have a party member who can fly, and Bombette can not be upgraded to Ultra Rank (allowing her to use Mega Bomb) this early in the game.