I have no idea how well the wood would hols up against the metal plate inside the click pad.
However, if you get any wood beater, DO NOT get the beaters in the link if you play any amount of double bass. They're too heavy. The wood beaters you have in mind will be significant'y lighter.
Gibraltar SC-3262 Solid Wood Bass Drum Beater: Shop Drums & Percussion & Other Musical Instruments | Musician's Friend