Beautiful carbine! I'd love to have a find like that! If you decide to clean it in any way, I'd suggest using an oil like Break Free CLP, a soft toothbrush and a very soft sponge to gently remove the loose surface rust. The oil will penetrate the surface to stabilize it and will leave a nice patina on the gun. I got really good results with it on an old rifle I found and it left a nice deep brown color to the metal. I recommend testing any method you might want to use on some old scrap iron such as railroad spikes first to decide which one works the best for you and also to see just how far you want to go with the cleaning.
I think if it were mine I'd search out a beat up old stock or buy a repro and finish it to look old and used to match it and display it as a complete gun.