Okay, it is your decision on whether to see a doctor or not. I've heard that once for hydrogen peroxide is enough. (More than that can slow down the healing process.) You could use soap and water initially. You can flush it with saline water after that first time. I found out about the Hydrogen Peroxide about 3 years ago. Betadine is good too, if you aren't allergic to it. I'm still a firm believer in Hydrogen Peroxide for the first thing I grab when I have a cut. Polysporin is what a doctor recommended I get for one of my kids in the past, so that is good.
Are you up to date on your Tetanus shot? I think you can still get that, especially if you cat goes outside.
If you were bit by a dog, cat, raccoon etc..., I've read Benzalkonium Chloride (BZK) is somewhat effective against rabies if you use it fast enough. If you are out in the wilderness and cannot get modern treatment, it is a good idea. I have those type of bandaids, that I bought at Walgreens. Check for allergies before you pack them in your bag though!
I get cat scratches now and then, but not a severe one. I have used Manuka honey for wounds a couple of times, it works wonders, and I healed faster than normal with it. Even if you have raw unfiltered honey, it is a great healing agent for wounds too. I have a well supplied first aid kit here. I mentioned that before, I know. One of the things I have in there is Manuka honey bandages. (different sizes too)