Learn English – “I’m happy to help”

You can almost always say "No thank you", which is polite enough on its own, but if you'd like to give a longer response, you could say something like:

No thank you. I appreciate the offer, but I'll be fine on my own.

Sometimes making your reply a little bit longer like this can make you seem more gracious and less brusque.

If you appear to be hurt, it would also be good to say "I'm okay" so they know not to worry.

In the absence of further context, I believe the definition of 'record' you are looking for is this one:

The sum of the past achievements or performance of a person, organization, or thing.

I believe that Hitchens is saying that Marvin Olasky is claiming that he has become a better husband since becoming a Christian. It is likely, as they are discussing religion (thus morality/ethics) in context to being a 'better husband', that he is refering to improved devotion/understanding/supportiveness/ faithfullness to his partner etc. So the sentence could be reworded as:

"He’s a convert from both Judaism and Communism. He tells the audience that since becoming a Christian he has become a better husband. I’m ready to believe it."