You can simply directly sub a diminished for the minor, if A minor, then sub A diminished. After all, a diminished sound is essentially a minor sound (at least to me). Your non-harmonic tones are b5, #5, and #7. The #7 is easy to deal with since it tonicizes the minor which is common to do on a "modal" tune. The other two tones are neighbor tones to the 5 so while they could present the trickiest dissonance, the resolution is on a very strong, restful tone.This is the most concrete advice given to the question. But the phrasing of the question misleads a little. The diminished scale (whole-half) works like the melodic minor scale. That's why it works with minor sixth or minor (maj7) best of all. Some may say I'm a purist based on this approach. But I've done my own research on all scales/modes that exist in the 12 tone system, and I would say that there are so many options for scales which capture best a certain harmony, why settle for something else?
The diminished scale over a C min looks like this C, D, Eb, F, F#, Ab, A, B; this has all the notes of the jazz melodic minor except the fifth (G), as
bob3dsf pointed out. Adding the G (which is present in the chord anyway) gives a 9-tone scale with very interesting properties. It includes the Hungarian Minor: C, D, Eb, F#, G, Ab, B as well as the 8-tone scale that I call bebop melodic minor: C, D, Eb, F, G, Ab, A, B. It has a portion of the blues scale: C, Eb, F, F#. It also has C harmonic minor, which means from the V7 chord G7b9, the Spanish scale (5th mode harmonic minor) is available. In fact the whole scale can be used modally (exclusively) over minor blues, no problem.
Chords included in this mode are:
Cm6, Cm (maj7), Cm(ma7)13#11
D7 (b9, #9, #11, 13) and then F7, Ab7, and B7 with the same color tones and alterations, also D6, F69, Ab6, B6; Dm6, Fm6, Abm6, Bm6
Do7, Fo7, Abo7, Bo7
Ebo7, F#o7, Ao7, Co7
Fm7, Fm6, Fm13#11
G9, G7(b13b9), Gmaj9
and some more.