Help! Cat neck wound

Help!
My cat, Chayce, got into a fight over food with my Chihuahua, Poppy. She left a wound on his neck, which bled, and I applied pressure on it until the bleeding had stopped. He doesn't seem to be in any pain, but it appears to be itchy as he keeps scratching it and re-opening the wound. I don't want it to get infected or not heal properly, but I'm not sure of how to properly clean and cover it-- or stop him from scratching it. Chayce is VERY fluffy, lots and lots of hair. So I cant think of any way to keep it covered. I was told to clean it with a mixture of warm water and peroxide to flush it out, I tried it once and he didn't seem to mind it but I don't want to continue if it's going to make it worse. Any suggestions on how to properly clean and cover it? And maybe something to stop the itching? Please help! Thank you!

It may be a blessing that it is itchy, the scratching may keep it open to drain. The itching is a sign of a scab forming, and hopefully healing. I've had so many abscesses on my cats from bite wounds it seems never ending, I'm taking care of one right now. A peroxide flush is done once, no more or it will cause tissue damage. Then there are sprays made for cats that can be applied, but now you have to watch for signs of infection or abscess. Swelling, a lump, or heat from the site. If this happens an antibiotic is in order, most can be got from your vet over the counter, if not you might have to bring him in. I would just keep an eye on it, there is no need to cover unless active bleeding is going on, spotting is fine. If it bleeds more heavily the area should be shaved and a dressing may have to be applied around the neck, or a stitch may have to be done at your vets.  The area should have the hair snipped away from around the wound, the hair may be causing some itching too. It would also make it easier to clean and inspect. 

I'm a little worried that you have a dog that actually draws blood from another domestic animal. Being the 'pack leader' I hope you made sure he knew this was not to be tolerated, the next step is a child being bitten in the face if they get too close while he is eating. I would definitely feed them separated from each other, and observing for any escalated aggression from either and putting a stop to it. Usually disputes like this are settled with growls and snapping, not outright violence. Accidents do happen of course, you know your animals better then any one else and are obviously a concerned caregiver or you wouldn't have come to this site. All the luck, and healing vibes your way!   

Thank you so, so much! This helps a lot. Would you happen to have any suggestion as far as the sprays you've mentioned for after the peroxide flush is done?

I've had both my chihuahua and Chayce for years and this has never happened-- ever. It really took me by surprise and I would have liked to assume it wouldn't happen again, but after it happened once, it happened again and now Chayce has two different wounds. The second time haven't even been a feeding incident. This hasn't happened once in the years I've had them both and right now I've just been watching them and feeding serparate. I would hate to have to rehome my chihuahua but if need be I have a parent close by to take her.

Thank you so much, again!