I'm thinking of giving away my sons cat
What makes you want to give away your son's cat?
Yes, I've been feeling guilty about this for a while
You should consider the reason that you want to give away your son's cat. It's cruel to give away a pet that your child is attached to. Doing so will make your son feel like you do not care about his feelings.
My son will get over it.
It is still wrong of you to do this. Your son will feel devastated. Don't do that to him.