[Andy]

I'm very right-handed, but it was drilled into me when I started umpiring that the mask is always removed with the left hand, so that's what I did from the beginning. I don't remember it feeling awkward or difficult at the time, now it's just natural.

One of our older guys who retired from calling a few years back always took his mask off with the right hand, then quickly transferred it to his left hand.
The only reason I know this is because he told me. He was so good at it and able to do it so quickly that by the time you looked at him, he already had the mask in his left hand. When I started watching him more closely, I was able to see what he did. I guess he just never got comfortable with using the left hand.