Get used to holding the razor with the non-dominant hand. It feels very foreign and unnatural at first. Slowly, with lots of concentration, shave the easy spots like the cheeks. Enjoy lots of success, build confidence, and then slowly expand the area you're shaving.

It's a process of training fine motor control with a hand that typically doesn't do much. For example, I can write with my left hand, but it looks very kindergarten-like. Likewise, folks who shoot handguns should invest time shooting with their non-dominant hand.