DD- This question has surfaced in the past. There was a proposal a few years ago to institute a "gunfighter" class. It failed approval of the Congress. So, in part, as a consequence, the proposal or question has not been brought forward again.
Realistically, since most of the stages are a departure from the usual 10-10-4, there are few "Gunfighter friendly" stages written. With many posses following a format that utilizes only a single pistol, and with the overwhelming response to such classes as Working Cowboy, and Originals, both of which utilize two firearms, there has been no demand for such a class, nor for stages that might be considered "gunfighter friendly".
Each posse is allowed to offer non-traditional classes or formats in their regular shoots. However, such allowances do not make for NCOWS approval as official unless voted in by the Congress. What this means is that you very well may be allowed to shoot "gunfighter style" at some club shoots, but it would not be expected at a regional or national level.
If there is a club near to you where you can participate, I suggest you ask them and see.