Okay, this is not the most fun you’re ever going to have. SoupAddict tried to spin this task every which way, but couldn’t find the “fun” angle.
But here’s the only angle that really matters: shelled shrimp, under normal selling circumstances, will remain fresher longer than peeled. And even if you have a lot of shrimp to peel, you can kind of get into a rhythm, like when you’re peeling potatoes.
If your shrimp have not been slit, take a sharp paring knife or a pair of scissors and cut along the outer curve, down to the tail.
As you probably suspected, “vein” is a nice, neutral word for what it really is: the intestinal track.