It is challenging to definitively determine the fastest sword style as it can depend on various factors such as the individual practitioner's skill, training, and physical attributes. Different sword styles emphasize different aspects of speed, agility, and technique. However, here are a few sword styles that are often associated with quick and swift movements:

1. Iaido: Iaido is a Japanese martial art focused on the art of drawing and striking with the sword in one fluid motion. It emphasizes quick and precise movements to execute techniques efficiently. Iaido practitioners train to achieve speed and accuracy in drawing the sword, delivering a decisive strike, and returning the sword to its scabbard.
2. Kendo: Kendo, also known as Japanese fencing, is a modern Japanese martial art derived from traditional swordsmanship. Kendo practitioners engage in sparring matches using bamboo swords called shinai. The emphasis on speed and timing is vital in Kendo, as practitioners aim to strike their opponent's target areas with swift and precise strikes.
3. Eskrima/Kali: Eskrima or Kali is a Filipino martial art that incorporates the use of various weapons, including swords. It focuses on fluid and rapid movements, utilizing both single and double sword techniques. The style emphasizes quick strikes, intricate footwork, and efficient body mechanics to generate speed and power.
4. Siljun Dobup: Siljun Dobup is a modern Korean martial art that focuses on sword techniques. It emphasizes speed, agility, and coordination through dynamic and rapid movements. Siljun Dobup practitioners train in quick drawing, slashing, and blocking techniques with a focus on efficiency and speed.

It's important to note that speed is not the sole determinant of effectiveness in swordsmanship. Factors such as timing, accuracy, technique, strategy, and the ability to read and react to an opponent's movements also play crucial roles in sword combat. The best approach is to find a sword style that aligns with your interests, goals, and training preferences, and then invest time and effort into honing your skills to develop speed and proficiency within that particular style.