I shoot M1c's and M1d's left handed, no major dramas. Just have to be a bit extra careful to not cant the weapon. Shooting both eyes open (which I generally do w/ everything) make keeping things upright easier. I've found Japanesesniper rifles are the hardest to shoot whilst maintaining zero cant, BTW.
I also have very little use for the cheek pads from either shoulder, so they usually get removed.