I found it not too big of a deal to master the motor skills part of shooting weak side. The problem for myself was training my non-dominant eye to get used to looking down the sights.
About 5 years ago, I developed a (hopefully short term) disability where my right elbow became useless, taking a good chunk of the function of my right arm away. I managed to learn to shoot lefty. I am right handed and VERY right eye dominant.
I would go to the range with a .22 and plink away. First with a scoped rifle, then once I had the hands and shouldering thing down, switched to iron sights. That took some serious doing. But I'm right eye dominant and you won't have to deal with that. Now I can shoot equally well left or right.
Now, I have regained enough of my right arm to shoot right handed standing and sitting, but ony left while prone. When I shoot BPCR Silhouette, I do chicken sighters left, then stand and shoot right. All of my lay down targets are still shot left. When the time comes that I get everything in order, It will take me some time to get used to shooting right handed, but I will still keep up the southpaw shooting.
Oh, one more thing. Your left shoulder is not conditioned to shooting... get a PAST girlie pad to ease the transition. Good luck.