I don't know if it's just me, but those two skills seem to have some headaches involved. First off, what differentiates 'staying cool" from "staying disciplined"? Both seem to involve roughly similar effects after all. Judging by descriptions I suppose Cool covers "noticing under stress" while Discipline is "dealing with stress"; that seem right to folks?
Cool as an initiative thing for "preparation" also really does not work well in my opinion. Basically explorers, scoundrels, and doctors are the best at ambushing someone, while a trained soldier or (worse!) a sniping assassin, is much better off if they are not prepared for a fight! Right now the combat specialized careers would do well to never plan ahead.
But the social interactions are what really drive me a little bonkers. For one thing, nobody can have both Cool and Discipline as class skills without specializing out of career, which seems a bit strange. I suppose there's an element of "nobody can resist every approach" to that which is good, but which class is effectively more resistant to a particular social skill thanks to skill distribution of Cool/Discipline works out just plain screwy. Politicos, supposedly the most specialized for social skill use, are without out of career spending hopeless saps, easy to deceive or sweet-talk (unless they become doctors and become resistant to sweet talk for some reason). They can dish it out but have no innate resistance beyond one fairly late talent. Smuggler/Scoundrels may not be charmable, but they fall for lies quite well, while the Hired Gun cannot be tricked but melt to any sob story; this seems almost backwards to the traditional "crook with a heart of gold" and "foolish guards" stereotypes.
Anyway, am I over-concerned with how those skills work out in actual practice, or is there some tweak that could fix things? On the social skill front, I've considered whether you should be able to use the same skill to oppose a social check (i.e. Charm vs. Charm) like Negotiation currently; Cool and Discipline would still have somewhat of an edge since you could resist multiple social skills with one of them, but at least a liar would recognize his own. Failing that, I'd at least swap the "Knowledge: Core Worlds" skill in the Politico specialization for one of those two so the Politico can come up with some defense against non-Jedi mind tricks. The Cool initiative thing I'm unsure of how to deal with; it has issues as noted but it kind of nerfs Cool to remove that role and give nothing back. Maybe instead swap things so Vigilance works for prepared attacks and Cool for surprises; it would make sense that scoundrels and explorers are more prepared for things suddenly going wrong on them, while combat professionals are more dangerous with prep time. Or maybe choose either of those skills for initiative but which attribute you use depends on circumstance (i.e. Cunning with whichever skill for prepared strikes, Willpower + whatever for walking around the corner into a pack of bounty hunters)?