Especially for a repeat offender, I really don't see what informing the dog owner is going to do except stir the pot. To me, it's just encouraging drama. I mean, for a repeat offender, I've already warned them.  If they still refuse to contain their dog, talking to them prior to the shooting wasn't productive, so I really just don't see what good would come out of talking to them about it afterwards. And anyway, if the repeat offender has again let their dog out, and one day it doesn't come back, they should know what happened to it, we already talked about it. I guess I feel I'd be gloating if I called them up and said, "hey your dogs were here again and I shot them". Calling them and telling them, "hey your dogs were here again and I shot at them, and I'm not sure if I got them or not", didn't work.  I'd only tell them I shot their dog out of anger, and I'm going to try to refrain from doing that. 
If I'm expected to "let it go" when their dogs attack my livestock then they can "let it go" when I shoot their dogs for attacking my livestock. After all, the golden rule does apply. Do unto others. Maybe they don't really want to know? If they want me to shut up, go away, and get over it, then they should too.
As for the random stray dog (which have always actually been good farm dogs in my good luck), I wouldn't know who their owner is the first place. Why would I go seek them out and tell them I shot their dog? They might go crazy, and again, drama drama drama. I wouldn't just shoot a visiting dog unless it was attacking something anyway, and if it's attacking something, it really is NOT my problem that it was so-and-so's best friend.
If a dog was in attack mode on my property, and if the owner was running behind it going insane trying to get a hold of it, unless it was massacring one of my dogs or kids or family members, I would give the owners the opportunity to contain it and have them reimburse me for any other damages. 
For me, I just don't get why someone would further stir the pot by seeking out dead dog owners and telling them all about it. For me, that's just antagonistic. If I'm not wanting to stir the pot, or not angry, I probably wouldn't tell them even if they asked. Again, I don't see what good can come of it. They're not going to go nuts wondering about the dog, because they know what their dogs are up to and they know how people feel about it. To me, if my neighbor with the prey-driven dogs let her dogs out ( and believe me, she knows what they're up to) and I shoot them, and she starts calling me asking me if I've seen them, I'd say she's looking for an arguement (as usual). 
I don't think it's kind to inform them, I think it's just giving them something to mill over and chew on.
We all have our ways of dealing with things. If you can't sleep at night because you're worried about dog owners worrying over their dog that you just shot. Then you SHOULD tell them for your own peace of mind. I can certainly understand that.  But I think it's cruel if you just want to stir the pot.  
My reason, and for me, it's a good reason: I would SSS to avoid adding fuel to the flames. Bad things already happened. No one wins when someone's animals invade your property, threaten or actually kill one of your own, and then you have the burden of kill the invading animal. It's stressful enough to kill a dog, not a pleasure. I'm not one of those people who will be elated and excited, especially if it's not killed with the first shot.  I will be very upset. Why make yourself more upset by adding drama into the equation?