At first I couldn't figure out shaving with the non dominant (left in my case) hand but forum member Danny Wonderful posted a tip on practicing shaving with the left hand while watching TV or sitting at the computer.

This was what got me over the hump. When I tried to do it during the actual shave looking in the mirror would confuse me. By practicing without looking I got the moves down. So I shaved with both hands a bit but went back to dominant hand shaving. It is just so familiar and I have no problems with it.

If I were ever to have an injury to my right hand or arm and couldn't use it to shave I could get used to using the non dominant hand. Of course that would depend on my being able to stretch with the injured member. No stretch, no straight razor shave.