I do artwork with paper and wood or metal all the time. I would use Golden (it's a brand) matte gel medium. Depending on the stiffness you buy, you may have to dilute it with a small amount of water. Apply a thin coat with a special tool that I call a cut-up credit card, using it sort of like a trowel. You may need to put a little medium under any edges that are loose, but it sinks in from the top, protecting the paper, and it may go through. You can also use a brush, but it will leave brush marks. Think decoupage.
Gel medium is archival, so it won't yellow or destroy the label, and it won't change the color. Practice with similar materials to get a feel for the process before you jump in, but it's doable and should be relatively undetectable as well, especially through a soundhole. You won't need more than a tablespoon of the medium--probably much less, but you do have to practice--so if possible, borrow a jar from a friend. Good luck!