I covered smaller sized variants extensively in a post I made a few months ago. The general consensus is that you should 110% wear what you want (which I already knew going in). Here’s a link to it: https://www.reddit.com/r/Watches/s/TqLUXfQR4p
One thing to consider is the thickness of the watch. Generally, if you want it to slip easily under a variety of long sleeve shirts, it should be as close to 10mm (or under) as you can find it.
It’s legit
Truly a blurry picture you have there. However, I think it’s this watch: https://www.tagheuer.com/us/en/timepieces/collections/tag-heuer-aquaracer/41-mm-quartz/WBD1112.BA0928.html
You can also buy regular leather straps that have been pressed into a crocodile grain. These would be a great option to test drive the look without spending a lot more money for the real thing. Link to a reputable shop: https://holbensfinewatchbands.com/pages/search-results-page?q=Crocodile