The leave it as suggestion is a good one. An old rifle seldom looks good with a new finish. Replace the parts that need replacing, especially the "scout" sight, and give 'er. The tape is most likely the result of a missing pin that holds the mag tube in place, or a worn dovetail. That rifle would not have had a "proper" barrel band on it. Also, depending on the vintage, it may have had the 32 rear sight on it. These were significantly different that the ramp and buckhorn style. Run the Googler on "Winchester 32 rear sight" for pictures.
Lots of ways to clean it up, without having it refinished. Having said that, were you planning on doing the work yourself?
R.