Let's look at more of the context:
Romans 10:9-11
That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. 10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. 11 For the scripture saith, Whosoever believeth on him shall not be ashamed.
I don't believe this passage means one must physically speak the confession in order to be saved. I believe the point is that the decision in the heart AND the words one speaks (or the signs one uses) must match. That is, if you truly believe in your heart that Jesus is your Savior, you should want to "confess" (meaning tell other people, thru spoken words, or signs, or written notes) that belief. It also means, if you say that you are a Christian, you must also believe that in your heart. Your words/actions must match your beliefs. If your words/actions don't match what is in your heart, then you are either a hypocrite or lying to yourself.
If you are truly saved, you won't be ashamed to let other people know that.
"For the scripture saith, Whosoever believeth on him shall not be ashamed."