When I say cool, I don't necessarily mean in fighting. The coolness could be from different categories. Basically I don't want a bumbling idiot who's always clumsy and falling down. It could be that she wears cool clothes (suit, jackets, etc) or is well educated with a good job or can think rationally. It could be any genre but I want it together with romance

The woman on my mind when writing this is An Di from Ode to joy she was so cool to me

OTJ%2B1.jpg

P.S I would like to avoid K-dramas as much as possible

Kimi wa Petto
Nang Rai Sai Lab

Even though it is Korean I would also recommend Ugly Alert. She owns her own business, is strong willed, and she is next in line to get the family business.
Of course you might disagree, but I found the female main characters of these dramas pretty cool:

Scent of a Woman
W
I Hear Your Voice
Doctors

(sorry these are all k-dramas - and I just noticed that you've seen I Hear Your Voice, but I'll just leave it in the list so you know what I consider a "cool" character)

For the j-dramas, I honestly don't remember them that well but I think these might apply:
Anego
Last Cinderella
I also second Kimi wa Petto