I would leave it as it is - yes it has patina but it’s honest character and goes with the unpolished case.
Personally I would put that on a tan suede strap - almost calling out the patina by matching the dial spotting to the strap... :-)
Something like this:
http://www.vintagestraps.it/leather-watch-straps/vs-hand-made-suede-beige-leather-strap/