Like others said, they're likely trying to determine that you're not a flipper or some other odious character. While I dislike this practice, it's better than having to buy a bunch of watches you don't want in order to build up a history.

Good luck. I think that both sizes will work for you, and it will just come down to your personal preference.

Not much reasonable that you can do other than selling it (or trying to see if the seller will allow you to return it) and getting a smaller size. Sorry.

There are different sizes, but you know that you can size it by removing links, right? It's like a regular bracelet with pins.

I think that a lot of replies are glossing over the whole "I'm interested in anything funky and digital as getting mechanical chronographs now a day is too pricy as far as i know." If you want something relatively affordable that still evokes the '62-ish era, I'd just google "mechaquartz racing chronograph". There's practically a cottage industry of vintage inspired racing chronographs with mechaquartz movements for <$500 (often <$300). If you want something digital or totally quartz and funky, the Seiko Giugiaro watches (as mentioned by others) are a great choice and have been mostly reissued, so they're easy to find in good shape.

For example, the 38 in blue purple on a 5.9" wrist:

Ultimately, there's no substitute for trying the piece on, especially these long-lugged Nomoses (Nomi?). One's wrist measurement isn't all that helpful for judgement calls, because the shape of the wrist can make all the difference. My wrist circumference is smaller than yours, but I tried on both 36 and 38 Club Campuses (Club Campi?), and the 38 made a whole lot more sense. My wrist is relatively flat / oval, so there's a nice landing pad for long lugs (plus, the lugs have a good wrist-hugging curve to them).

Check out the Nomos site, where they have pictures of the watches on wrists accompanied by actual wrist measurements. You'll see examples of people perfectly rocking the 38 with sub-6" wrists.