Mink oil or any leather conditioner will darken it. Surface will become smoothed out though. Asso is always nice with some suede texture on it. I'd say wear it out for natural patina.
i did my rep asso, and my caitlin 2 with olive oil, use a paper towel to do it, and control the amount you add, and gradually bring the darkness to your liking... this worked out REALLY well on my Cait 2, ill take pics of it this evening.
I am glad some of you got the results you were looking for, but PLEASE do not use olive oil or baby oil. Just because something might look alright, doesn't mean that it is the proper way to go about it. Invest in a good leather conditioner/wax from Pecards or Lexol (a small tub will last you a lifetime). Olive oil will gunk up the fibers and will in a short amount of time oxidize and go rancid. The same with Baby oil.
I have an asso strap. I have no problems with it. It is smooth and fits well. Do not use olive oil or baby oil. Over time this will kill the band. As many have suggested, please invest in a small tub of leather conditioner