If you are anything like many people, then you have become accustomed to assigning one hand the majority of any tasks requiring fine motor control while your 'off' hand is consigned to a lesser assistance roll (grasping, holding, supporting).

The difficulty in using the 'off' hand for any task is really a matter of actually using it and training it. It is not just the movement of the hand, itself, but also a matter of training the 'off' arm to respond properly as well. When learning to shave, just work at it slowly and only to the point that you still feel comfortable... and safe.

I have gone through the same routine and while sometimes a slow process it is not impossible. I favor my right hand, and involving my left hand and arm in the process has been slow going. The smooth, hand-eye coordination developed over years of constant use of the major hand needs to be trained into the 'off' hand and that can really feel like work (literally). Especially in the beginning, the task of controlling the 'off' hand for me felt very tiresome and I found myself returning to using my right hand after only a few shaky strokes with the left. Well, I kept at it and although it is not yet the equal of my right hand, my left hand is now definitely of some use when I shave.

Best advice: practice, practice, practice.