I like to put a generous coat of Kroil oil on all the metal but one must be careful not to get it on the wood. You can use wax paper or whatever to keep it off the wood. Let it sit a few days. Scrub and wipe it off with a Kroil oil wet cotton cloth. Reapply as needed. Apply RIG after cleaning.
The conservative alterative is to just apply Rust Inhibiting Grease/RIG to all metal and try to keep it off the wood, although it is fairly harmless to wood since it is wax based. That will widely slow the rust.
I would not shoot the bnz. Buy an RC for shooting.
You can do nothing as many may suggest. If you do that where I live you will have massive rust and mold on the wood in a year or so unless you have a temp and humidity controlled environment, which is the most important thing going forward IMO, to both wood and metal.
All that said, listen to the experts here. Many collectors like them just as you have them. Then, just store them in a temp and humidity controlled environment.