I shaved with my left hand only for about the first 3 months when I started wet shaving. There were spots that I could not get the correct angle on my neck. I tried various grips on the straight before eventually giving in to using my right hand as well. After a couple weeks I was confident in my non-dominant hand and do not think I could shave with a straight without using both now.
I still only use my left for lathering and DE shaves.