Portuguese Blue aligator strap care

I've had my blue portuguese automatic for a few months and the strap has become dull/matte towards one side and I've come to the conclusion that I need to clean/polish it back to its new shine.

I've done a bit of research and I think I should look to polish it using some natural beeswax. I've found the following two polishes on sites on the net, would anyone recommend one of these? and if so which one?

www.dotsapothecaryshop.co.uk/di/219297

www.thehoneydoctor.com/acatalog/BEESWAX_POLISH.html

(note: the shoe polish on the above page not the furniture polish)

I really appreciate all your help with this. Thanks.

Richard.

Why not just try one, using just a little on a small portion?

As a shoe salesman while I was in college, I used Venetian Cream --but I think many neutral leather conditioners should work.