There is no purple sword in Wii Sports Resort. The Swordplay mode (Duel, Speed Slice, Showdown) uses only the standard beige/brown wooden practice sword and the glowing blue/red team indicators in multiplayer. No color variations, unlockable skins, or purple blades exist in the game code.
If you saw a purple sword in a video, it was likely a mod (homebrew), a different game, or a visual artifact. Provide more context (game mode, single/multiplayer, video source) if you want help identifying the actual source.