Your worship can be a witness. Acts 2 tells us the early church praised God and enjoyed the favor of the people, and "each day the Lord added to their fellowship those who were being saved" (verse 47). Is that somehow suggesting there could be a connection between worship and witness? I think so.
I think it is a powerful testimony to the world when a Christian can praise God despite hardship. Christians lose their jobs. Christians get cancer. Christians die in automobile accidents. Christians lose loved ones. Christians face all of the hardships that others face. But when people see Christians praising God despite the adverse circumstances, when they see us honoring the Lord, that is a powerful testimony.
I came to Christ initially because I saw a bunch of Christians worshipping the Lord on my high school campus. I was just a kid with no direction in life, and as I was walking across my high school campus, there was a group of Christians sitting on the lawn, singing songs. They were really simple songs. There was nothing aesthetically attractive about them. But what interested me was why they were singing songs about God at lunchtime on the front lawn of my high school campus. So I sat down far enough away where people wouldn't think I was joining them, but close enough where I could eavesdrop on what they were doing. And as I watched them sing these very simple songs about God, I was moved by it. It opened my heart to hear the Word of God proclaimed.
I think the same was true of the early church. They worshipped the Lord, and it was a powerful testimony. You see, worship and witness can go together. Our worship can be a witness.