You don’t play a lot of minor chords in Western Swing, but what is very common is the B part going to the relative minor. A typical B part, in the key of C, goes:
|Am/E7/|Am///|D7///|G7///| or
|E7///|Am///|D7///|G7///|
So either way you get that second measure with the relative minor, Am, to fool around with. I don’t have a lot of shtick for this situation, but here is what I often play. It is written as block chords, but I would play bass-strum. In place of the E7, you could play Bm7b5 (7x776x), or E7b9 (7x676x). B diminished sounds pretty good too.
Code:
Am E7 Am E7
----5---------------------------
----5---------------------------
----5-----7-----9------7--------
----7-----6-----7------6--------
----7---------------------------
----5-----7-----8------7--------
Similarly, if the minor chord has its root on the 5th string:
Code:
Dm A7 Dm A7
----5-----5-----------5---------
----6-----5-----6-----5---------
----7-----6-----7-----6---------
----7-----5-----7-----5---------
----5-----7-----8-----7---------
--------------------------------
Here is a one measure walk down:
Code:
Dm Dm/C# Dm/C Dm/B or Dm/B
---------------------------------------
-------------------------------6-------
----10---10------10----10------7-------
----7----7-------7-----7-------7-------
---------------------------------------
----10---9-------8-----7-------7-------