No, you cannot change swords in Wii Sports Resort. The Swordplay mode (Wakeboarding/Chambara) uses only a single, standard fencing foil for all duels and challenges.
If you want varied swords and combat progression, try these Wii titles:
Wii Sports Resort excels at accessible, pick-up-and-play motion controls, but for RPG-style weapon progression, look to the games above.