Songs that exude cool? Polka Dots and Moonbeams by Lester Young. Young was not only cool, he actually coined the phrase. Here's Lester. No passage work. Just melody.
If you can't stick jazz no matter who plays it, here is Boz Scagg's T-Bone Shuffle which I like over the original.
If you only think of cool in teen-age terms, here's Let Her Dance by Bobby Fuller. Why is this cool? Think about it: his girl broke up with him and his response? Good for her. There'll be another along soon. Backing voices are like the sunrise. (Legend has it that Terri Garr is one of the Shivaree dancers.)