Here's some artists/recordings that you might find will produce the balance between pure jazz and jazz/blues that is not too improvisational. Don't forget the very important role female artists played in both jazz and blues right from the very beginning and many of their recordings are a perfect blend of jazz and blues known as "torch music" and are highly listenable such as older artists like Billie Holiday, Sarah Vaughn, Alberta Hunter, Shirley Horn and newer artists like Sade, especially her "Love Deluxe" album which to my mind is the perfect blend of cool, melodic jazz with a nice emphasis on the sax.
As far as male artists, maybe give a listen to Dr. John, Louis Armstrong, John Mayall's "Turning Point" album featuring John Mark and Johnny Almond, Boz Scaggs, Stan Getz with Gato Barbieri for an intro to South American jazz, and finally and surprisingly, the band Traffic on their classic album Low Spark Of High Heeled boys. All of these artists produced very listenable, accessible jazz with a touch of blues.
Hope these can help you and don't forget the females.