Ballistol will probably work but I think I'd just rub it out lightly with a good coat of raw linseed oiland some fine steel wool. It'll clean and preserve it without removing the original patina.
If you want to really clean the wood without damage, use Dollar Store clear ammonia and a Scotchbrite sponge/scrub pad carefully, rinse with water, dry thoroughly and oil with raw linseed as original. The patina will come back PDQ with several coats of RLO.