I'd give my right hand to ambidextrous....
Is a very old joke. There are very few folks who are ambidextrous (Question: Is there such a thing as ambisinister? Yes).
Handedness - how you hold a tool can completely change the way you work. Sometimes a left handed approach to cutting or paring can make a huge difference compared to moving a piece around and re-clamping it to work the same cut from a right handed position.
Much of my work is sculptural - I spend a lot of time with rasps and files to blend surfaces together. For example in blending the base and stem of this piece I consciously practice using my left hand to rasp and file the profile. I've found that over time I've got a lot more dextrous with left hand (that almost sounds like an oxymoron).
So I urge you to try using you left hand (or other hand) whenever you can. Recently I've been painting the windows in the new bench room and I've found it easier to switch hands than contort myself to always use my right hand. Similarly I found it much easier to switch hands to use the razor blade scraper to clean up the glass.
I find that I can use use light tools more easily in either hand but have a tough time using a cordless drill driver in my left hand. Guess I'll just have to row some more and build up my strength.
My father was left handed and always lamented that nobody else in the family was left handed (though my brother started out left handed) - so I imagine he's having a little chuckle now.