In this previous post I discussed the resolution of non-altered V7 chords in major keys.
Let’s see what happens in minor keys, and also how we need to approach altered dominant chords (in major and minor keys all the same).
So you have the complete story!

1. Non-altered V7 chords in minor keys.
The resolution V7 – i (e.g. G7 -> Cm) is the same as V7 – I (G7 -> C): F goes to Eb and B goes to C.

All the options discussed in the previous post are still valid, with the following caveat: on the Cm chord (C Eb G), a natural E is an absolute no-no! While it is often possible to play a b3 over a major chord (that happens all the time in blues), you should never play a regular 3 over a minor chord – it sounds horrible!
For that reason the Lydian dominant scale (G A B C# D E F) cannot easily resolve on the Cm chord (but it can of course resolve on the G7 chord).

But the minor scales offer other modes that we can use profitably in a minor context.

1.1. The Mixolydian b13 scale
This is the 5th mode of the melodic minor scale.
Starting with C melodic minor: C D Eb F G A B, and taking the 5th mode, we get G A B C D Eb F.
In terms of chord tones and tension, we have R 9 3 (11) 5 b13 b7.
The 11 is (as usually) an avoid note, but the chordal b13 is the minor third in C minor, so this scale is easier to handle in a minor context because the resolution is possible on G7 as well as on Cm.

1.2 The Phrygian dominant scale
This is the fifth mode of the harmonic minor scale (and the standard scale in Flamenco!)
Starting with C harmonic minor: C D Eb F G Ab B, and taking the 5th mode, we get G Ab B C D Eb F.
In terms of chord tones and tensions, we have R b9 3 (11) 5 b13 b7.
This scale gives us a b9, a very nice tension note on a V7 chord.

2. Altered dominant chords
Altered dominant chords contain a b5 or a #5 in place of the natural fifth. For example: G7(#5,b9) = (G B D# Ab). Altered dominants are frequent in jazz and classical music and also (to some extent) in pop, but much less so in standard blues.
The natural fifth should be avoided on those chords because it clashes unpleasantly with the altered 5th.

There are several possibilities, but the easiest is probably the altered scale.
The altered scale is the 7th mode of the melodic minor scale.
We start with the Ab melodic minor scale: Ab Bb Cb Db Eb F G.
Taking the 7th mode we get: G Ab Bb Cb Db Eb F.
Bb is enharmonically equivalent to A#, Cb is equivalent to B and Eb is equivalent to D#. So we respell the scale G Ab A# B Db D# F and we get R b9 #9 3 b5 #5 b7.
This scale gives us all the tones we need over the altered V7 chord: (R, 3, b5/#5, b7, b9/#9). But it does take some practice before you start to feel comfortable with it…

Conclusion
All this scale business (the modes of the minor scales) doesn’t need to scare you. Scales are just tools to make music and in this case they are simply a way to get interesting tension notes. You can see them as prepackaged tension devices for V7 chords.
The important things to remember as improviser are:
– the fact that a V7 chords need to resolve (and why this is the case!)
– the available tensions (and avoid notes) on a V7 chord, and how those notes behave in the current key
It is quite possible to simply play a pentatonic scale and add some specific tensions on the V7 (e.g. the b9, or the 9, or the b13) and resolve it properly, if that’s what you are comfortable with. That’s often the way Brian handles it.