kridenow,
It seems that your experience w/ adventures are somewhat different from mine, but then again, I've only been using published adventures from ICON & Decipher so far. However, I should add that Star Trek scenarios generally do seem to have more social encounters than other RPG genres. It's just been my experience that most of the published Star Trek scenarios call for more non-social tests than social tests.
My personal preference as a GM as always been to roleplay social encounters rather than rollplay them. So if the PCs want to bluff the Cardassian guard, negotiate a ceasefire w/ the Dominion, or uncover rumors on DS9, I look to see how well the player can do it first b/f rolling dice, if at all. However, I've found that some players just aren't very good at that sort of thing. Some just can't bluff well or come up w/ an persuasive argument quickly. So for those players I let them roll the dice & just say "I try to bluff the guard," or "I try to Influence the ambassador," or "I look for rumors about the recent heist." It's not my preference to do it that way, but allow it when the player can't do it him/herself.
Even though a Starfleet vessel has more non-military positions than today's Navy, I'm sure every Starfleet officer would receive basic training in emergency procedures & combat situations. I can't imagine that Starfleet would not expect all officers & crew on a ship to have some sort of function in an emergency (combat or otherwise), whether it be damage control or tending to casualties or even auxiliary security.
So for those PCs who don't have a lot of "military" or engineering skills, give them a duty to do in an emergency situation. You can work w/ the player to find out what job their character would best suited for whenever the ship goes to red alert.