This is an example of a non diatonic functioning diminished chord in another well known standard song, As Time Goes By, starting at its bridge:
Whether the changes are correct or not, you are facing this onstage, sight reading. There is no way the A diminished chord is acting as a diatonic functioning chord, since it is not followed by a half step or the same root. See my workbook.
You must be able to see the chord tone of A dim7. Seeing a chord tone right away is essential to improvisation. Once you see a chord tone, you should see four dominant chords:
The note on the A dim7 chord which does not appear in those four dominant chords becomes tension. Let's examine.
Any one of them will work. You pick one that you like, and blow away.