You might find your left hand does more than you think. Try not using it for a while. Put it in a pocket, tuck it in your waistband or don't put your left arm through a sleeve and keep it and the hand inside clothing.

Pay attention to how often you're frustrated because you've been using your left hand for ancillary work all along and now you can't do any of that.

Ancillary work is often as important as the main task.

And part of the problem with trying to use a non-dominant hand for a dominant task is that the dominant hand also has little-to-no idea how to do the supporting non-dominant work properly.

NB: If you do decide to artificially gimp your left arm, however, uh, 'armlessly, do take care not to fall over or have some other kind of mishap. At the first sign of tempted fate, ungimp that arm.

Edit: With apologies to those rare folks with only one good arm who have been getting by without any kind of ancillary arm help for a significant period of time, and with genuine sympathy for those who've recently actually lost the use of an arm.