Fox, I get what you're saying about the squads, but the word "squad" by definition implies more than one person. The headhunters, like you said, are a two man group. Two is still more than one. If one of them is KIA (Or MIA. "Spartans never die"), then the remaining member is no longer part of a squad.
Those who go solo are typically called rogues, lone-wolves, operatives, or freelancers, depending on their overall affiliation and classification. Rogues typically are unaffiliated. Ex-military, disbanded, discharged, etc.. Basically the people who are no longer a part of nor welcome in an official group. A lone-wolf can be a rogue, but a lone wolf can also be affiliated with a group, just not part of a team. Master Chief, for example, would be a lone-wolf, as he is still part of the UNSC but he acts and is most often deployed alone (at least in-game). The difference between a lone-wolf and an operative/operator is that a lone-wolf is usually solo because he/she is antisocial or by any other explanation "does not play well with others." Operatives typically are those whose objective is best accomplished solo. Scouting, infiltration, sniper, or those who would have been issued the JFO configuration in Reach, being the ones who have to get up as close to the enemy ranks as possible to identify priority targets. A lot easier to do with one Spartan than with a whole squad. Freelancers on the other hand are more closely related to rogues, but while rogues tend to operate on their own and for their own purposes, freelancers are often willing to put their skills out for hire. Basically a "higher class" of mercenary.
So with those definitions in mind, I would probably have to classify myself/my Spartan as an operative with lone-wolf tendencies. lol. I can work with a team, but prefer solo most of the time, and my tactics generally gravitate towards a more solo methods (long range sniping or tactical approach as opposed to guns blazing, shock and awe, or overwhelming firepower tactics).