You Have Options.
I have a lefty friend who does what you suggest.
You could always learn to shoot right-handed, which you should do, anyways.
Another option is a car holster. I have one that attaches beneath the steering wheel, as I don't want to damage the bucket seats of my Porsche. There are others that attach to the front of the seat.
Member: Orange Gunsite Family, NRA--Life, Varmint Hunters' Assn., ARTCA, American Legion, & South Cuyahoga Sportsmen's Assn.
Caveat Emptor: Cavery Grips from Clayton, NC. He is a ripoff