YOU CAN PLAY IN THE SAME KEY AS NAT KING COLE IN GCEA TUNING, IF YOU PUT YOUR CAPO ON THE 3rd FRET! It's a great, slow exercise in diminished chords, but if you're having difficulties, don't forget you can always simplify some chords, e.g., [Dm] instead of [Dm7], [G7] instead of [Ddim7], the 2 finger first inversion of [C#dim7] instead of the 4 finger 2nd inversion. The diminished chords can be barred but James Hill recommends using all 4 fingers, e.g., for the [Ddim7] you would put your 1st finger on the 4th string 1st fret, 2nd finger on the 2nd string 1st fret, 3rd finger on the 3rd string 2nd fret, and the 4th finger on the 1st string 2nd fret. The reason for getting into the habit of this is that it makes it super easy to swing into the jazzy chords - keep your 1st and 2nd fingers in place, but slide your 3rd and 4th fingers up one fret and enjoy that lovely sound!
"Smile" is a song based on an instrumental theme used in the soundtrack for the 1936 Charlie Chaplin movie Modern Times. Chaplin composed the music, while John Turner and Geoffrey Parsons added the lyrics and title in 1954. The lyrics are based on the lines and themes from the film. "Smile" has become a popular standard since its original use in Chaplin's film.
A video for this song: