PMCs still specialize in combat. You could also have specified the absence of rank in the military CS. The Science CS is for scientists that research the kaiju or other types of experts that focus on saving civilians and acting as envoys between countries, e.g diplomats, linguists, doctors, aid workers and psychologists. Not necessarily just a civilian. An actual [i]expert[/i] on civilians. I think that's what @Polyphemus meant to say.

I'm not sure if ordinary civilians can just join the White Gloves just like that, unless they have at least some combat experience (thus making them part of the military department) or can contribute some sort of intellectual ability (thus making a part of the scientist/civilian expert department. Using a military CS does not necessarily have to mean your character belongs to a national army. 

It's not actually that hard to switch CSes. Just have to add in a rank field and military branch field. Sort of like this:

Rank: There are usually no ranks in PMC companies.
Military Branch: Schults does not belong to conventional armed forces. Rather, he serves as a senior member of the Silver Talons, a private [i]military[/i] company. (You also might have to specify what type of combat they specialize in. Sea? Air? Land? I'm probably guessing land, but it's possible for PMCs to specialize in all of them at once)

You can leave the Alma Mater field in if it's really relevant.

P.S Commander Walter? If there are no ranks, say Walter is the "leader". Otherwise, Commander could be a particularly tenacious nickname to whoever's in charge.