I am Left dominant, hand, eye, foot, everything.
when young, I was forced to do most of the usual things [eating, writing, etc.] right handed.
I learned to shoot a rifle right handed because it was a semi-auto.
And, I believe that I was encouraged to do so.
I have always owned a semi-auto, so it has never been an issue, except for having to close my left eye to be able to sight it .

I taught myself to shoot a hand gun left handed in order to to be able to use my left eye for sighting.
It works great!
I'm glad I did it.

I have recently had glaucoma surgery on my right eye.
I put it off so long that there is nerve damage. 
I will never be able to sight a rifle with my right eye again.
It was  never the best option anyway.
I can hunt with the hand gun,but would like to keep the rifle option open.

So, my main concern is flying brass into my face when shooting the SKS left handed.
It may be an almost non issue.
If I remember correctly, it does fling the brass a bit forward rather than back.
But , there is always that stray that goes somewhere else that concerns me.

Any southpaws here that use right handed semi autos, SKS in particular?
If so, what is your experience with it?

1 more week and we will be starting our trip out of Alaska heading for HI.

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The bringing my firearms to HI has been worked out.
I'll mail the rifles to myself at our storage unit on BI.
My hand gun is going to a FFL in Moses Lake, WA  where my son lives.
I'll pick it up there and bring it as checked baggage when we fly over from San Diego.
The only question left is:
Is the arrival of the rifles before I do, and their being there a few weeks before I arrive an issue with the 48hr registration requirement?

I'm a southpaw and I use only "right handed" guns.

Whether its a shotgun, rifle or pistol, I've never had a problem with any brass.

My advice is right or left handed, wear safety glasses and a good hat when shooting firearms.

1v1 I was trained to use both dominant and weak, it came in handy for me once.. It's always good to practice ambidextrous training...

Once I started shooting pistol, I concentrated on shooting right handed being right eye dominant.  Was not too hard when really first starting without much muscle memory to overcome.  Been left handed forever, although a touch ambidextrous.  Most semi pistols being designed for right handed shooters made the switch easier.

Now I am retraining decades of rifle shooting left handed to right.  Several reasons, right eye dominant part of it, want a bolt gun, etc.

Shooting precision targets with a pellet rifle is helping set the memory in place.  Looking back, I could have just trained in boot camp as a right hander and never had issues since I had not fired a rifle before that.

It is all about muscle memory.  Oh yeah: a decent pellet pistol is a great training aide and cheap.

I didn't specifically retrain myself, but I can shoot either way.  Some days I shoot better on my weak side.

I routinely practice shooting with left hand and left eye, right hand and right eye.

You never know.