True worship is when God's people worship Him in Spirit and in Truth, "God is spirit, and his worshipers must worship in spirit and in truth."  [John 4:24]
 
An unbeliever cannot be a true worshiper for he is not indwelt by the Holy Spirit and he does not accept, nor does he have the truth of God within his heart and mind.  Jesus said, "He who is not with me is against me, and he who does not gather with me scatters."  [Matthew 12:30]
 
This unbeliever who plays in your worship service is an enemy of Christ, thus he cannot offer any worship that is acceptable to Him.  His sacrifice of praise is not acceptable to God, "...the sacrifices of pagans are offered to demons, not to God..."  [1 Corinthians 10:20]
 
If you truly love this person and care for his soul, then you would make it clear to him that he cannot be a part of the worship, because he is still lost in his sins and condemned to hell.  If he is offended and leaves the church that is fine, for an unbeliever does not have to come to church to be saved.  God saves His elect when and where He wants through the ministry of the Word--through the message about Christ (Rom 10:17).  If this man is elect, then God will draw him to Christ when it fits His divine and perfect plan.
 
One of the real problems today in the church is our concept that we have to get the unbelievers to come to church in order to be saved.  This is a very dangerous belief, for the church is not for unbelievers but for the saints.  We are to equip the saints to live godly lives so that they will be a creditable witness as they go through the world in their daily lives.  They are to win people to Christ away from the church, and then bring them to the church when they have been saved to be baptized, and then to be taught all that Christ has commanded (Mat 28:19-20).