It is just usually used to name a character that seems attractive...how ya didn't catch it? "there are some characters that ppl find appealing or attractive because of their looks" I wrote...
The appeal/attraction in looks, the cool demeanor, the usually confident attitude & the arrogant poise, is defined as 'having swagger'.
'Having swag' is just a stupid abbreviated slang; that doesn't have the same meaning. Even Justin Bieber sees himself as someone full of swag; which is as laughable as the above Urban dictionary definition.
As for your question, well, I named some that I find having swagger in looks and attitude (as for 'swag', I'll be in support of that word, the day it gets a proper dictionary definition.)
Spike Spiegel: Self-explanatory.
Kamina: The shades, the cape, the tattoos and that arrogant smile. What else?
Kakashi: I think he's a mix of class and swagger but the mask is a great point for the latter.
Gaara: The long dark-red coat, those kanji tattoos, kohl in eyes, that arrogant voice and the sand attack... Awesome!
Atem 'Pharaoh Yugi': Those spikes hairs, those clothing & a gold 'fu**in' Millennium Puzzle in your neck...
Seto Kaiba: Millionaire & arrogant to the max with the most godly jacket that I've seen in Anime...Do I need to say more?
There are also some cool characters that I find more class than having swagger and some that has an undefined level of awesomeness & coolness, that they are in another medium than class/swagger. Atleast, that's my take.