I use asymmetrically ground razors almost exclusively (mostly folding razors, with the occasional fixed blade for variety), and use whichever side of the razor suits the job (although I only use my dominate hand so nearly all strokes are with the omote against my face).

If you have shaved for a while (and/or use different razors regularly) the adjustment needed to use either side is almost unnoticeable. What you will notice is the difference in grips that can be used between a fixed blade and a folding blade, but that is itself not too hard to get a handle on.