You can learn to left mouse. If your mouse is ambidextrous already, move it over to the left of your keyboard and try it for 30-60 minutes a day for a couple weeks. I like left-mousing at work and right-mousing at home (strange I know), and when I left mouse, I prefer the buttons flipped (index finger always is 'left click', etc).
If your mouse is right-hand specific, try getting a ambidextrous one next time. Most of the ambidextrous mice these days are gaming mice, but they work fine for pushing cursors around too.