I often buy raw king prawns (maybe they're called shrimp where you are, they're about 3-4 inches long) - they are already shelled and beheaded, but they've still got the blue vein running down the middle of them. My current technique is to put the point of a sharp knife just under parts of the vein and then pull it out, kind of like unpicking a thread of cotton. This takes quite a while, there must be a better way..? Is butterflying a way to achieve this?
I usually slit the prawn flesh just above and along the line of the vein to expose it and to make it easier to then pull out.
This is different from butterflying a prawn, which involves a deeper cut (but not all the way through) of the prawn along most of its length along the same line as the de-veining cut, but also leaving the tail on usually.
This video shows the de-veining technique and the butterflying.
Have you tried the basic cheapo shrimp deveiner? A little practice, and it's actually quite effective.
Score across the back as you mention and then scrape out the vein under cold running water using either a knife or your thumb.