In Ephesians 5:19, we are to be "speaking to ourselves". This is done by singing AND making melody in our hearts. Those are two separate things, which is notified by the use of the conjunction "and".
In Colossians 3:16, we are to be "teaching and admonishing one another". This is also done by singing. While we are singing, we are told to have "grace in your hearts to the Lord".
You are "commanded" to sing and make melody "in your heart." Period. Nothing in that sentence suggests that you are allowed to sing or make melody with your mouth. The word "mouth" or "voice" is nowhere to be found in that verse or any other verse. So any singing or melodies must emanate only from the heart. You are not authorized to use your mouth.
Now I suspect that maybe you might be able to move your lips as long as you don't smack them together and make some noise that might be misinterpreted by the other parishoners as being "joyful". But it is clear from that verse that the only practice that is specifically "allowed" or "authorized" is singing and making melody in your heart. Obviously if you sing with your mouth it would be the functional equivalent of changing the tires when you are only authorized to change the oil (or other such nonsense).