Actually, *proper* Christian witness (not the coercion that some Christians *think* is witnessing) has respect for reason and individual choice. Yes, it does start from the premise that a specific belief system is correct - but there is a fundamental respect for the rights of others to choose alternate paths.
If this is what we mean by "witness", then yes - I think that UU witness is a great idea. Obviously the specifics would be a bit different, but the overall ideas are surprisingly similar.
A good example of a code for proper Christian witness is the IVCF's Code of Ethics for Christian Witness:
As Christians called by the Living God, we seek first of all to honor Him and His ethical standards in all of our private and public lives, including our efforts to persuade others to believe the good news about Jesus Christ.
As Christian evangelists, we seek to follow the mandate, motives, message, and model of our God who is always pursuing and reclaiming those who are lost in sin and rebellion against Him.
We believe all people are created in God's image and therefore endowed with the capacity to be in relationship with their Creator and Redeemer. We disavow any effort to influence people that de-personalize or deprive them of their inherent value as persons.
Respecting the value of persons, we believe all people worthy of hearing the gospel of this loving Lord Jesus Christ. We equally affirm the inalienable right of every person to survey other opinions and convert to or choose a different belief system.
We believe in the gospel of Jesus Christ, and affirm the role and goal of the Christian evangelist. However, we do not believe that this justifies any means to fulfill that end. Hence, we disavow the use of any coercive techniques or manipulative appeals which bypass a person's critical faculties, play on psychological weaknesses, undermine relationship with family or religious institutions, or mask the true nature of Christian conversion.
While respecting the individual integrity, intellectual honesty, and academic freedom of all other believers and skeptics, we seek to proclaim Christ openly. We reveal our own identity and purpose, our theological positions and sources of information and will not be intentionally misleading. Respect for human integrity means no false advertising, no personal aggrandizement from successfully persuading others to follow Jesus, and no overly emotional appeals which minimize reason and evidence.
As Christian evangelists, we seek to embrace people of other religious persuasions in true dialogue. That is, we acknowledge our common humanity as equally sinful, equally needy, and equally dependent on the grace of God we proclaim. We seek to listen sensitively in order to understand, and thus divest our witness of any stereotypes or fixed formulae which are barriers to true dialogue.
As Christian evangelists, we accept the obligation to admonish one who represents the Christian faith in any manner incompatible with these ethical guidelines.
I stand corrected.