Help! Chicken attacked by dog - Help or put it out of it's misery?

This seems to be a popular topic - chicken attacked by a dog. I JUST adopted this rooster today from someone off BYC and I feel like a horrible person! He got out of my coop/run - NEVER have any of my hens ever escaped! And they climb all over the dang thing - and when my husband tried to catch him he flew over the wall and into the neighbors dog run. The neighbors have chickens as well and were extremely kind and gentle with my roo when they were able to get him away from the dog. I apologized profusely, I feel horrible! I don't have any idea how he got out, but now he has been hurt.
He looked dead at first, but he is still breathing and he has opened his eyes. He lost a lot of feathers and he is pretty well covered in slobber. I found one super small possible puncture on his underside, and the skin above one of the wings has be torn along the shoulder. A little but of the fat got torn, but the muscle and meat underneath are completely intact. It mostly just looks like the skin is torn.
I have no idea what to do. I don't know if the chicken is dying - the wound don't seem that bad at all, but of course he could have some organ damage or internal bleeding I can't see - or if he is just in shock and so is sort of drifting in and out of consciousness.

I used some cloth scraps to kind of lash his wing to his body but the slash through the skin is in such an awkward place I can't really keep it together. Do I need to rinse it out? Should I put anything like triple antibiotic ointment on it? Should I super glue or stitch the skin back together?
Or should I just let DH ut the thing out of it's misery? I will get pictures as soon as I can

UPDATE - he passed away last night. Thank you to everyone for trying to help him!

 

I think this one ^ is the best representation of location. You can see it's right where his wing attaches on his back that is ripped open







After washing him off better, I did notice some scrapes and a big puncture on the other side under his wing. Washed those out as best I could. Should I get a curved tip syringe and flush out the puncture wound? I can bring one home from work, but all I have to wash it out with is water. I really cant pick anything up until I get paid on Friday, so I'm stuck with water and hydrogen peroxide - I don't think I should our that into the wound though should I?




The puncture ^ is the one closes to my thumb. you an see right under the skin possibly into a cavity through that hole, it is much deeper than the photo shows.

 

Unfortunately he died last night. I don't know how I'm going to tell the nice people who gave him to me. He was the only baby from their favorite chicken who passed and hoped I could bring back some of his offspring. They just couldn't keep a roo in the city.

Thank you all for your good wishes and information though! I'm sure it will help if this ever happens again.