You cannot obtain a silver shovel in Animal Crossing: Wild World because the game was released on the Nintendo DS, not the Wii. The silver shovel debuted in later titles like Animal Crossing: New Leaf and New Horizons.
In Wild World, the only shovels available are the regular shovel and the golden shovel. Here's how to get the golden shovel:
Persistence is key; keep checking glowing spots daily until you find it.