I need to describe a certain scene from the POV of an assassin, and I'd like to use the terms that she would use. Think ninja assassin, rather than Mata Hari.
Traditionally, no. Assassins tend to try to blend into their surroundings. Otherwise, they would get caught. The actual ninja is often presented in modern film/TV as wearing an all-black costume. There's no historical evidence for this.
That makes sense, really. If someone walks into town dressed as a murderer, they're going to be arrested, stopped, or killed by the authorities. You don't want to label yourself as an assassin. You want to blend in, so you can sneak up on your targets and, hopefully, sneak away after killing them. So you'll don whatever garb is most likely to get you close to your target.
You want to be invisible in to the extent possible. That doesn't mean black costumes. That means dressing like the servants no one pays attention to. Or like a homeless person on the street. Or like the palace guards that are everywhere.
The original assassins were a Middle Eastern sect of the Medieval era.
Assassins is the description used to refer to a group of individuals of the medieval period known as Nizari Ismailis. Often enough described as a secret order led by a mysterious "Old Man of the Mountain", the Nizari Ismailis were a sect that formed in the late 11th century from a split within Ismailism – itself a branch of Shia Islam.
The actual assassins in this sect were low-level followers: --
While "Assassins" typically refers to the entire medieval Nizari sect, in fact only a class of acolytes known as the fida'i actually engaged in assassination work. Lacking their own army, the Nizari relied on these warriors to carry out espionage and assassinations of key enemy figures, and over the course of 300 years successfully killed two caliphs, and many viziers, sultans, and Crusader leaders
This description of the assassins and how they worked clearly demonstrates they worked secretly and as unobtrusively as possible.
Although the "Fida'yin" were the lowest rank in Sabbah's order and were only used as expendable pawns to do the Grandmaster's bidding, much time and many resources were put into training them. The Assassins were generally young in age, giving them the physical strength and stamina which would be required to carry out these murders. However, physical prowess was not the only trait that was required to be a "Fida'i". To get to their targets, the Assassins had to be patient, cold, and calculating. They were generally intelligent and well-read because they were required to possess not only knowledge about their enemy, but his or her culture and their native language. They were trained by their masters to disguise themselves and sneak into enemy territory to perform the assassinations, instead of simply attacking their target outright.
The last thing any assassin needed was an assassin's uniform or distinctive form of clothing. A dress code for assassins would be a dead giveaway.
PS: You might like some background history on the origin story of assassins.