I highly recommend against neatsfoot oil. It breaks down the fibers in leather and can ruin leather, either by making it wear quicker or whatever. I feel that it may bring down the value a bit if someone knows it has been oiled that way. It also has a specific smell that seems to never go away. I purchased a used Devoucoux bridle that seemed to not have been well conditioned recently but had that neatsfoot oil smell on it. I resold it as the leather wasn’t nice looking and I personally do not like neatsfoot because of the smell and what it does to leather.
I recommend contacting CWD to ask what they think is best for the leather.
Based on my experience as a nice-quality-leather-fanatic, especially if it is calfskin or buffalo, I highly recommend Leather Therapy Restorer and Conditioner. It makes most leathers buttery soft and definitely has darkened a few things for me. It also serves as a wonderful conditioner to maintain the leather and its condition. CWD leather balsam seems to not darken as quickly, if at all, and saddle company’s leather care products are just really expensive in my eyes for not being “magic.”
I have heard well of olive oil. If you want to use a true oil, that’s the one I would try. But I would try the Leather Therapy over this - I swear by their products (including their “wash” cleaner)!