The Fighting Style of Balrog aka Vega aka Claw from Street Fighter is a mixture of Ninjutsu and Spanish Bullfighting and probably the Historical Spanish Fencing Martial Art La Verdadera Destreza.
Ninjutsu is a Japanese Martial Art Strategy based on Stealth, Assassination, Espionage, Warfare and Tactics. The Ninja did use Firearms especially since Guns were imported to Japan from Portugal. While their existence is debatable they did play a part in Japanese Martial Arts.
Spanish Bullfighting is a type of Bullfighting practiced in Spain, Mexico, Peru, Ecuador, Colombia, Venezuela, it's also practiced in France and Portugal. It's also the Bullfighting that Balrog aka Vega aka Claw practiced. He combined with Ninjutsu to make Spanish Ninjutsu.
La Verdadera Destreza is a Historical Spanish Fencing Martial Art. It's primarily a System of Swordsmanship. Jerónimo Sánchez De Carranza is credited as the creator. It was a break from the Older Spanish Fencing Traditions that predate it.
This new approach to Spanish Swordsmanship was either derived from or influenced by Italian Swordsmanship. Balrog aka Vega aka Claw's Style may have combined this too. Especially since his original design is a Medieval Style Masked Spanish Knight.
Overall from what I see the Fighting Style of Balrog aka Vega aka Claw from Street Fighter Spanish Ninjutsu is a mixture of Ninjutsu, Spanish Bullfighting, and La Verdadera Destreza.
One of the well Known Ninja Weapons is the Tekko-Kagi which is the Weapon that Balrog aka Vega aka Claw uses in the Games. This is also the Weapon Geki from Street Fighter 1 (Street Fighter I) used in 1987.