You must be referring to Dudley Dursley in the first Harry Potter book. If so, in Chapter 3, “The Letters from No One” Dudley is preparing to go to Uncle Vernon’s former school, named Smeltings. The book describes the uniforms worn by the boys there, which Uncle Vernon had to buy for Dudley, and it says the boys “also carried knobbly sticks, used for hitting each other while the teachers weren’t looking.” I imagine they would be similar to walking sticks. The name comes from the name of the school, “Smeltings”. So that’s what a “Smelting Stick” is.