Image stacking in dim light

One possible way to improve image quality when shooting in low light is image stacking.  Take a series of shots with the same settings without moving, use software to align the images and then use software to average (mean or median) the aligned images.  This decreases noise and therefore increase signal to noise ratio.

Another image stacking technique is focus stacking. Take a series of shots with the same settings without moving, except vary focus, align and stack into layers and then use layer masks to keep the sharpest area of each shot.

I'm wondering what the best stacking technique would be for shooting in dim light when you want lots of depth of field and you don't have a tripod or other means of bracing.  One alternative is to shoot at a small aperture with a high ISO and stack to limit noise.  Another alternative is to shoot at a larger aperture with a lower ISO and focus stack.

Any thoughts on the relative merits of the two techniques in this situation or whether some other technique (but not a tripod or other bracing) would be better?

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