First of all, "ninjutsu" is not "sword fighting" but rather "Art of the ninja/art of deception".
What you're referring to is Kenjutsu, which is one of the 18 disciplines of ninjutsu.
Also, traditional Kenjutsu doesn't generally focus on Katana's. Katana's were a samurai's weapon, and Samurai's were all about honor; Ninja's were not.
Kenjutsu would likely teach you how to use a Ninjato, and small daggers. Unlike a Katana, a ninjato is shorter and straight. It does however have the same basic properties. It has a dull side, and a sharp side as well as a slanted single-edged tip made for cutting rather than stabbing. These weapons are for quick slices, rather than full out duels.
"Traditional swords" as you say depend highly on which country.
I'd recommend one of two things.
Either learn fencing, which is more of a "sporty" blade combat sport.
Or learn Historical European Swordsmanship, which is basically Knights Swordsmanship.
http://www.swordsmanship.org.uk/index.ht...
That's a website to give you an idea of what European Swordsmanship is.
Just remember, regardless of what you choose don't call it "Swordfighting" or people will consider you ignorant. You're learning Swordsmanship (Way of the sword) not "swordfighting".
If you're in the UK, just go for HEMA (Historical European Martial Arts). They'll teach you how to fight with longsword, saber, sidesword, polearms, rapiers, etc.
There are plenty of fencing clubs around the country.
You may get useful answers by switching the category from the US to the UK.
Look for a fencing club near you. You can learn foil, epee, or sabre (three different swords).
