The way I understand it, SPECIAL was a way of having GURPS in a video game without copyright infringement. I could very well see SPECIAL as "universal" system if you're willing to dispense with levels.
To the point, BRP is a percentile skill system that's pretty basic as well. You have attributes which determine starting skills. You distribute your points from Education or Intelligence or whatever into your skills. In Call of Cthulhu, you never level up and your skills are largely limited to your profession with wiggle room for "hobbies." Skills are improved by actually using them.
In Traveller, progression is very rare, because it assumes that you've left a military branch and became a merc. As such you're actually middle-aged by that point and only "progress" with dedicated training or correspondence courses. Your stats are largely your stats and you make do with it. (Amusingly enough, your character can die in character creation since it's supposed to simulate the evolution of character's history.)
As such, I feel Star Trek generally works best on a skill model, not a leveling model, because it isn't a picaresque about gaining personal power. It's a very idealistic setting and Federation officers tend to be already-accomplished professionals, bordering on the best-of-the-best. They don't follow the conventions of a hero's arc like Luke Skywalker or lust for personal wealth the way Conan might. They've abolished money after all and are largely a post-scarcity civilization.
The 7 attributes would make the transition basically unscathed (though you'll have to think about what role you want "luck" to fit in your notion of the Trek universe), but you'd want to edit the skills a lot, since all weapons are energy weapons, there really aren't any locks to pick, and most everything you'd do on a starship would fall under "science." You would probably be better off just scrapping the existing skills list and just coming up with a list of skills you think would be relevant, and putting them on a 100 point (i.e. "roll under on a d100") scale.
That isn't very difficult to deal with. As with Call of Cthulhu it really depends on how you compartmentalize different skills in a way that makes sense to the setting. Even within Fallout, guns got collapsed from "Small Guns" and "Big Guns" to just "Guns" in NV.
Call of Cthulhu also has different splat books and provisions for time periods. For example, "Chemistry" wouldn't exist in the Dark Ages, but "Alchemy" would. Speech can be "Diplomacy" or "Fast Talk" or "Credibility" or "Social Status" and can be as granular or general as you like.
Science can be divided up into stuff like "Astrophysics," "Biology," and so forth. Or "Medicine (Human)" and so on.