You would still need to exert pressure with your right hand, to hold the ruler. You might be able to overcome that problem by using weights. But my rotary cutter can be used by left and right handed people. I just have to reverse the blade and screw.
I think it would be more of a dexterity issue. Are you very right handed or do you often do things with your left hand, like stirring a batter, pinning a seam, picking up necessary objects?
You could try out your idea with your current cutter, a ruler and some paper (much cheaper than buying another cutter and using fabric for a test)