I'm working on a Stargate story, and I've been wondering about Civilian Contractors. In our real-world military, civilian companies are playing an ever-increasing role in the military, performing all kinds of technical and logistical roles on bases, and even very near the front lines. Did we ever see that happening in the SGC? That's an operation that has to be WAY outside the usual role of the Air Force--they're exploring worlds with strange plants and animals, weird tech that's either primitive or hyper-advanced, deciphering alien computer code, circuit schematics, and medical techniques... they can't have been doing all that with personnel who had spent most of their time training to fly and maintain aircraft, could they? Did they ever show specialist civilians inside the SGC? Would it be that much more dangerous to trust a civilian (bound by every Non-disclosure agreement imaginable) than to trust an airman who has sworn an oath to keep those secrets?
Yes, at least on individual levels. The most prominent example, beyond Dr. Jackson himself (who is of course, a civilian, although you might consider that a special circumstance) and pretty much all of the alien members of SG-1 who don't fit into the existing military structure, is Dr. Rodney McKay, who has pointed out on several occasions that he's a civilian, including in his first appearance, the episode "48 Hours." At the end, they suggest that they're reassigning him to Russia.
McKAY: I am not going to Russia. Do you know what the food is like in Russia? Besides I'm a civilian, I don't have to do what you say.
CARTER: Well as long as you're on the Air Force payroll.
McKAY: Oh.. this really sucks.
We've also seen on several occasions individuals who are asked to sign an NDA so they can consult on one issue or another, or be approached for a more extensive job. McKay's sister Jeannie is one who didn't want to sign the agreement (until she was just told what it was for).
As for companies, it depends on what you mean by "working within the Stargate program." We have seen several instances of civilian companies that work on technology related to the overall defense of Earth from alien threats (and the cover-up involved), such as Coulson Industries, which both cleaned up Antarctica from the battle over the Atlantis outpost, and developed an engine control system for the F-302s.
There was also Devlin Medical Technologies, which kidnapped Rodney and his sister.
McKay: They're a predominantly government funded contractor and, unfortunately for us, they manufacture our subcutaneous transmitters."
"Government-funded" is a little ambiguous and so may arguably be not "civilian," but I think it counts. In any event, they, and other companies, are often used to get alien technology out to the public (once suitably sanitized and a paper trail supporting their "discovery" is created), and although they often have access to some information that is classified, usually they're not told the whole story and do not know of the Stargate itself.
It seems that the general pattern is that they'll hire civilian contractors on an individual basis and give them fairly high access (contingent on NDAs being signed, etc), when needed for their expertise on the front-lines but for companies they'll keep them on a need-to-know basis and keep them working on pieces of a larger whole, like for supporting their space-vessel construction.
While there may be contractors companies who are more in the know, and it's possible some are even working directly at the SGC in Cheyenne Mountain, we don't seem to see any direct evidence of this.