https://www.amazon.com/Bickmore-Bick-Leather-Conditioner-Finished/dp/B001CS2Q4M
You only need the first part. Could you edit your links to make them not gross? Thanks!
No, please don't. That's an oiled leather and would not look good with a wax/polish.
You need a shoe brush. Buffing with it briskly will heat the leather and the natural oils will come up to the surface and even out the scuffs and lighter spots.
If that doesn't do it fully:
I use Bickmore No. 4 on oiled leather, as it doesn't normally change the color. Lots of leather conditioners will darken. Brush lightly after drying for an hour or so.
If that isn't enough I also use Saphir Greasy Leather Conditioner . Get the uncolored one, unless you really, really, think you need to add color. Buff after letting them sit overnight.
Light applications of both, you can always add more later.