Shot glass, photo shot, "I'm shot" (I'm exhausted), the air conditioner is shot (it's broken)--"shot" has plenty of non-violent connotations. But jab--there is nothing non-violent about the word--I don't want a measles jab under any circumstances! But I'll be glad to get a measles shot. ;-)
All US origin usage. Shows how much part of American thought patterns it is.