My question was:
"Can you find a scripture (other than in the Gospels) that either specifically says or even implies that laymen are directed to witness to the unsaved?"
The above does not answer the question. So you could not find a scripture that directs laymen to witness to the unsaved. Apparently, there is no scripture that says or implies that laymen are directed to witness to the unsaved. Perhaps someone else knows of a scripture that answers the question.
Of all the instructions that Paul gives to the churches in his letters, I don't think the issue of laymen witnessing to the unsaved is addressed.
Rev. 22:17 And the Spirit and the bride say, Come. And let him that heareth say, Come. And let him that is athirst come. And whosoever will, let him take the water of life freely.
1Th 1:8 For from you sounded out the word of the Lord not only in Macedonia and Achaia, but also in every place your faith to God-ward is spread abroad; so that we need not to speak any thing.
Rom. 16:19 For your obedience is come abroad unto all men. I am glad therefore on your behalf: but yet I would have you wise unto that which is good, and simple concerning evil.
Finally, the command to be witnesses unto all nations is part and parcel of the apostolic doctrine or the faith once delivered that was taught all the congregations. The following phrases are synonyms for "the faith" once delivered: (The faith, The doctrine, The Tradition, The truth, The apostolic doctrine, The doctrine of Christ).
NE has the right or the privileges of Christian apostleship; it belongs to those commissioned by Christ in Person or secondarily and FINALLY, to those in turn commissioned by the apostles in person.