I personally wouldnt play mixolydian over this tune at all...Id play the major scale, Pentatonics (switch between major and minor) and arpeggios. oh and if used correctly the blues scale would sound nice
If you add the major and minor pentatonic scales together, you get a mixolydian scale plus the flat 3rd. There's a lot of blues licks that use these notes. You can also add the flat five as another "blue note". Using the notes in each chord and moving chromatically to them is also useful.