If you’re studying Japanese style fencing, you would call it Kenjutsu or Kendo. This is the use of katana or shinai. There is also the art of drawing your sword, called Iaido. Here you use a wooden sword called a boku. Archery in Japan is called kyudo.
For western style weapons, follow gail’s suggestions.
“The Iaidoka (a practitioner of iaido) wields a sword: not to control the opponent, but to control himself. Iaido is mostly performed solo as a series of Waza. The Iaidoka executes various techniques against single or multiple imaginary opponents. Each Waza begins and ends with the sword sheathed.” source
But Iaido does not use katana. I used to study Iaido and we used wooden swords. Advanced practitioners of Iaido use metallic blades made of zinc, but I was told that almost no one uses a steel-blade katana when practicing Iaido. The reason is because Iaido is a meditative single-person martial art where the “blade” is in close proximity to the body and the hands. A sharp blade could cause injury, for which there is no need.