The problem with overdressing (as an engineer) is that outside visitors will assume that you're not an engineer.
Like, you can be wearing the nicest of tuxedo pants with the nicest of button-down shirts, but adding just the right hat or scarf magically turns it into a casual outfit.
"Unconventional accessories are always a good pick" is playing with fire, as is recommending tuxedo pants, a button down, and a hat or scarf.
Have you seen what nerds do when told it's okay to wear hats?
But when I'm travelling overseas, it gets a much more positive and inquisitive reaction. Many times people have used the hat as an ice-breaker to start an interesting conversation with me. And if you're the only person with a hat in a group, it can be helpful branding so people recognize & remember you.