The shape is real, light travel time isn't a factor here. It only takes light ~100k years to cross the entire galaxy, but the motions that affect the overall shape of the galaxy play out over tens to hundreds of millions of years. For scale, it takes Sol about 230 million years to make one orbit around the galaxy.
So the galaxy is moving at 1.3 million miles an hour (although relative to what is a good question). So when light leaves one end of the galaxy and travels in a straight(ish) line to the other side... the other side isn't there anymore. It would be:1138.8 trillion (193ly) miles displaced.
So the light we see from the other side of the galaxy is light that started directed towards the point 193ly from where the galaxy was when it left if you follow me. So if the galaxy is moving "up" the light from teh other side of the galaxy actually came from 193ly below us.
It's a bit like Andromeda looks skewed to us because the light arriving from it's closest edge arrives 100s of thousands of years before the light leaving it's farthest edge and as it's rotating it appears distorted.
However in relation to the original question, I believe astronomers would have accounted for this.