I haven't seen "The Vengeance Factor" that I can recall; based on your description she posed an active threat to the crew and could not be arrested without risking the lives of crewmen. Perhaps the only way to stop her was to kill her.
There are two important elements to this that make the threat non-acute. One, Riker had already forced the innocent-looking killer Yuta to her knees with nonlethal phaser bursts, and keeping on doing so would have allowed the intended victim to be whisked to safety. Two, as she was engineered to be a biological precision weapon, Yuta was lethal only to her intended set of victims, not to people outside her hit list; Riker could have wrestled her down (at least after a few more stun bursts, and some help from his crewmates present at the scene) and restrained her for good. Any immediacy of threat was thus carefully eliminated from the scene, whether the writer intended it or not.
However, there are two other elements that make the threat unstoppable outside the murder option. One, Yuta had been programmed with the need to kill everybody on her hit list (which was down to one man now), and apparently could not have any sort of a life that would
not involve attempting to kill. Two, Yuta was extremely lethal to her intended victims, virtually immortal, and capable of shrugging off the standard Starfleet/law enforcement response of stun guns; the odds of her eventually succeeding were high unless her life was ended one way (death) or another (eternally clawing at the padded walls of her cell).
Riker chose to end her life with vaporization rather than permanent locking up. That this was not considered objectionable by anybody involved (not even Yuta!) tells volumes about Starfleet rules and UFP laws (even if those volumes are on a language rather alien to us!).
This was his only way to prevent more killing by Fajo.
The problem is, the audience knows this is not true. Data is a one-man army: starting out unarmed, he subdues an entire nation in "Ensigns of Command"! Fajo could be left unharmed aboard a ship torn to nonfunctional pieces, waiting for pickup by the authorities. Fajo could be immobilized. Fajo could be rendered unconscious. Fajo could be killed in such a fashion that resurrection by 24th century medicine would be trivial. Fajo could be tortured until he gave up his evil ways and wet himself in terror at the very thought of having to confront Data on the issue.
The episode would work well were Data replaced by a less powerful character, with the same ethical limitations. TNG had none handy, alas.
Timo Saloniemi