STOP! DO NOT USE LEATHER CLEANERS/CONDITIONERS.
What you show is a natural leather patina. And it looks beautiful. This is how ANY fine leather should age. Go ahead and look in high end catalogues. This patina is actually very desired, and people look forward to their leather looking like this over time.
Do NOT use leather cream/conditioners unless you have had experience with them in the past. A LOT of them end up damaging the leather, even if they come directly from the leather maker. There are many people that bought leather conditioners from Coach directly, complaining about it damaging their leather. It can either dry it out, crack it, or cause a permanent color change.
You will NOT be able to clean that darker brown out. That is not superficial dirt. That is likely wear, dirt, oils, etc. that have absorbed into the leather, and changed it permanently (for the good).
Enjoy your cuff, and don't worry about your beautiful product.