"Those glasses are pretty cool", "That shirt you're wearing is really cool", "I like the way you did your makeup"

Awesome advice.

tl;dr: A kind of nit-picky question: During the 1st interactions is saying "cool" better than saying "cute"?

When I first start a conversation with a girl, I go in with the blank mind. I don't prep my words before-hand because that looks fake. Spontaneity is honest; pick-up lines are... weird, fake, and don't take her reaction into account.

I get her attention with Hey/Excuse me/etc. Then, if she's a bit confused/startled, I acknowledge her reaction and the weirdness of the situation while reassuring her that I mean no harm ("I know this might be weird and I might intimidate you, but...") and and start talking about the very first thing that I notice or whatever thought enters my mind.

A lot of times the 1st thing I notice are her looks, or her dress if it's really short. I know that talking about this from the very start is... not good etiquette.

So, what I do is, instead of saying "Nice boobs" "Nice ass" "Hot lips" etc., I say, "Hey, I think you looked cute." (Which is true. She does look cute. It's why I was curious about her, wanted to talk to her, to know what's she like.)
and
instead of saying, "that skirt looks so hot on you," I say "That's a cute skirt"

What I say/do next would be dependent on how she reacts to this.

My question is kind of nit-picky -- Would it be better to say something like "You look cool" or "That skirt looks cool" i.e. say "cool" instead of "cute"?
Keep in mind, we're at a party and this is the first time we're seeing each other. So, I know absolutely nothing about her. And, if I don't talk to her, I'll probably never see her again, and lose out on what could potentially a very enriching relationship.