Something like the assassination of George Hasek is a tactical or operational move, because that alone will not accomplish the strategic objective. It may make the task easier, and may have a pronounced strategic effect, but ultimately you still need "boots on the ground" to take and hold the planet or continent, which is the actual strategic objective, and that will ultimately require at least a battalion of troops.
One Clansman convinced a planet to surrender, but it still took an occupation force to hold it, otherwise the surrender would quickly have become meaningless.
The question is a bit vague as to whether or not that organizational unit is expected to accomplish its strategic end goal by itself. I would have to say that a single person could conceivably conduct a "strategic operation" IN SUPPORT of a strategic objective, but the actual accomplishment of that strategic objective would ultimately require a significantly larger force. Such a small unit could NOT conduct a viable strategic operation on its own.
To examine another previous example, a dog runs out, the general's jeep swerves, and the general is killed. In the absence of a combat force capable of engaging the deceased general's army, the general is replaced shortly thereafter, and there is no significant effect at the strategic level.
In Croatia, a terrorist kills an heir to the throne of Austria, but without several countries ready to mobilize for war at the drop of a hat, there is no war. It is a tactical event with powerful strategic implications, but not enough of a force to carry out the following strategic operation on its own. WITH the inclusion of the powerful military forces preparing for what was believed to be an inevitable confrontation, it triggered a war unlike any the world had seen before.