Don't fear your other hand!
I had been a "right hand only" shaver since I started with str8ts, and all was quite well with that.
But the last two shaves I just all of a sudden decide to give the left hand a try also. It just flashed into my head "give it a try". I was pleasantly surprised that it went very well, and actually helped speed up the shave.
When I shaved with one hand only (see, I'm already speaking of it in the past tense!), I had to constantly stop and re-adjust my grip on the razor to reach the other side of my face, stop re-adjust to get in over there...no, that;s not quite right...here, let me try this....OK, now for over here, let me use the backhand Stanislav grip.....etc...etc.. you one handers know what I'm talking about here.
If you use both hands you can simply use the "classic" razor grip, and only switch hands to access the appropriate regions of your face.
Also, shaving with your "off" hand helps with the zen concentration aspects of the shave. Give it a try! The first time I tried it it was on pass 2 or 3, which was good, as sometimes if you have to plow through the underbrush on pass #1, it may discourage you.
I really felt that this was a significant improvement to my Shave.