I got a couple of perlon straps from cheapestnatostraps, the blue is a bit too much contrast but the dark green dresses it down a bit. You've probably got a few more options, not being the gold version.
I have a Bambino v3 in blue. I had it on a brown leather strap for a while, then put it on a mesh bracelet. May never change. The mesh bracelet doesn't necessarily dress it down, but I think it makes it more versatile.
For the OP.......The face has a nice classic style that will be hard to dress down as such, Like some women, they can dress in a hessian sack and still look good, I think your watch has that kind of look, no matter what you put on it from ****e to glitz I doubt it'll "dress down" it's just one of those watches.
Put ugly on it and it'll draw more attention, put beauty on it and IMHO you'll drawn the same, of course from folk that are into watches .
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