There's a line of thinking out there that sharing your testimony with unbelievers is useless; you need to call them to repentance. There is some truth to that statement. If the unbeliever doesn't realize that it isn't just something nice for you but rather is a command from God to everyone, then he may walk away without the burden that he, too, needs to believe. But that doesn't mean your testimony is worthless.
When Jesus healed the demon-possessed man, the man wanted to go with Him, but Jesus forbade it. Instead, He said to him,
"Go home to your friends and tell them how much the Lord has done for you, and how He has had mercy on you." (Mark 5:19)
Jesus commands the man to give his testimony to others, meaning to share with others what Christ has done for him. Whether someone could be saved or not by that testimony is not said in this passage. But what we can conclude is that sharing one's testimony has value, otherwise Jesus wouldn't have told him to do it.
What does sharing your testimony do? For other believers, it's encouraging. Unbelievers may not be encouraged by your testimony. But whether to a believer or an unbeliever, your testimony glorifies God. Praising God for what He has done glorifies Him, whether the person whom you're telling believes you or not.
And I also don't buy for a moment that someone listening could not be saved by listening to your testimony. Some think that unless there's a specific call to repentance, the listener can't be saved. But what is that based on? Do we not believe that someone could read through Ephesians and be saved? But nowhere in Ephesians does Paul call people to repentance. All he does is explain what God has done for him and the Christians in Ephesus. Even the book of John, which explicitly states that it is written so that people would believe and be saved, has no explicit command to its audience to repent and believe. Rather, it describes what Jesus said and did and how a person can be saved, and that is sufficient to save someone reading it.
I'm not saying it's wrong to call someone to repentance; the Apostles did it (sometimes) in Acts. What I'm saying is that your testimony is not worthless, and by listening to it, someone could be saved. And even if no one believes or is encouraged as a result of your testimony, it still glorifies God as you honor Him with your lips.