I would do it. first, because it is a good thing to do and you will gain reward for it if God wills. Secondly, because it gives a strong family structure to the community.
I see many guys on here saying that they wouldn't raise another man's sperm and all that but how do you know that your own blood children will turn out great? Blood doesn't always count for everything, sometimes your own family hurt you the most in life.
It might be that the kid that has a different father turns out to be a great person and a source of happiness and satisfaction for you. It's not easy to have affection for another person's child I understand, it's natural to feel that way. The path to heaven is hard though and is not meant to be easy.