What is the significance of Katana Swords being the weapon for Deadpool?

Deadpool uses ninja swords, katanas, because he uses katanas in the comics. It's adaptation tautology. He has had katanas since his first introduction in 1991. He actually mastered kenjutsu and how to use katanas the normal way. He was even a sumo wrestler for a while (not in a joke manner).

In the movie universe, it's because they look cool. Wade is all about looking cool. It's not supposed to be a deep reason.

From this

Deadpool employs any number of weapons depending on his current assignment. Most often, Deadpool uses guns, grenades, sais, knives, and katanas. Wade can use any weapon known to man and learn how to use the weapon in less than 5 minutes.

and from this

Although Wilson also uses guns from time to time, he seems to prefer taking out his swords as they've proven to be more lethal than any firearm

Purely in the movie, Wade is said to both be former special forces and a mercenary, making a good case that he learned close quarters combat techniques in the military. I don't think it's too far of a stretch to assume he used swords as a mercenary beforehand based on previous versions of the character (such as the referenced X-Men Origins: Wolverine) and his apparent experience with them. Or, if we asked Deadpool, he'd probably say he copied Deathstroke.

The Katana Swords are usually the best for the job and he does use similar weapons in the movie. He uses sharp weapons which re useful and are the usual thought of how to kill other than uusing a gun. Deadpool's powers are why is easily so acrobatic automaticlly. His powers make him a better marksman, allowing him to make his shots in akward angles. Deadpool's abilities expand far beyond just being an increased healing factor and immortality. Funny ability includes increased metabolismwith his real favorite food being pancakes. Deadpool is an insanely powerful mutant. The swords are a weapon that is easy to use and suits his abilities.

Obviously the movie hasn't told all of Deadpool's story (really, Wade's story for that matter), there's more material to pull from the comics. If you're sticking completely from the movies, his first appearance is NOT his solo movie.

Though may people disliked his story-line in the movie "Wolverine", he is shown there on a mission using the swords as well. This gives us evidence that he did indeed know how to use them before he became Deadpool, as well as suggesting they were his weapon of choice.

In the comics, Deadpool is a highly trained assassin and mercenary, and has studied multiple forms of martial arts. He is also a swordsman and marksman. At the end of the day, he uses swords because that's what the writers chose.