If I recall correctly, the mallet handle is in one of the barrels in the same room as the ward keepers (check them all and you'll come across it eventually--of course, you'll have to put the mallet together first before you can use it).
Each ward keeper requires you to fulfill a specific task (that is the so-called "riddle"); once you complete all the said tasks (you'll have to speak to each ward keeper first to get an idea what each one will need from you), you will need to speak to each ward keeper a second time to verify that the mission was accomplished (be ready for anything when you do--hint, hint).
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