Don't worry - unless you actually grab a corydoras cat and squeeze it, you will never be damaged by their spines. Even if you were, catfish that small simply do not have the venom capacity to hurt a human. They won't hurt your betta, either. They are extremely gentle fish. I have kept them with bettas for years, as have many other people, and I have NEVER heard of a betta being attacked by a cory.
However, I'm not sure tankmates are the solution in your case - they may even have the opposite effect by stressing him out and causing him to be more reclusive. Have a look at other factors in your tank. What is the temperature? What is your cleaning schedule? What is the tank size? Does he have lots of things to hide in and play with?
When considering tankmates, there are a number of important factors. First, they have to be happy in your water. For instance, if you have hard, alkaline water, livebearers are good, but they won't be so happy in soft acidic water such as tetras prefer.
Secondly, the tankmate must not be aggressive or nippy. That rules out barbs, as you correctly said, cichlids, other bettas, gouramis, paradise fish, and even certain little schooling fish.
Thirdly, the tankmates shouldn't be too colourful or have very flowing fins - that may invite aggression from your betta.
Fourthly, your tank MUST be large enough to support tankmates - at least ten gallons!
Let us know if you have any questions. :)