This is what we're talking about when "caulking a boat" is the topic. It's done with the caulking irons and a caulking mallet. In the old days the caulk was actually Oakum, which is a product of the hemp family of plants.

The irons are varied in their design to get into different aspects of a boat's hull and decking. The two on the right are reefing irons, the others are setting irons, bent irons and threading irons. These mostly are marked C. Drew & Co. Kingston, Mass. This is in no way a complete set, I doubt there ever is one that would be considered "complete".

This mallet is mesquite with forged hoops on the ends and at the center. The handle is hickory.

Here is an image from the Maritime History Archive at Memorial University of Newfoundland. It shows the caulking mallet in use.

One distinctive feature of a caulking mallet is the slots cut into the head. If i recall correctly, I was told that these provide less vibration to the handle and extra amount of "spring" or rebound in use, thereby making the job a little less fatiguing. Can't speak from experience though, so I'm trusting the old salt that told me.