Yet if we require someone to be punished who has sinned against us how can we claim that we have forgiven them ?
What you are asking is not unlike asking, "Are we are God?"
The answer is, No, we are God's, and do not forgive in the way you have asked the question.
It is God who forgives sin, and yes we are called to forgive our brothers, but also called by God to seek and support justice by those appointed over us by God. Which in certain times even means yielding to the laws of evil overseers--even as Christ did by going to the cross. So then, if we would consider it best to be turned over to punishment (as did Christ), the only godly alternative to turning those who have done evil to us to the authorities, would be to allow their punishment to be placed upon us...as He did.
Is that what you are proposing?