Prior to pandemic, I wore my OP all the time in the subway. No issues.
After pandemic, subway crime has increased. I work from home 95% of the time. When I take the subway to work (in Soho), I wear my SS Rolex if I have a sleeve covering it. If I wear short sleeves, I have my non-SS Rolex in my bag and then take it out to wear when I'm in the office.
Since it'll still be warm when you visit, your wrist will be exposed and green bezel/dial will stand out.
When I picked up my yellow gold Day-Date from the NYC RSC last month, I wanted to wear it immediately but the two RSC reps didn't recommend it especially if taking the subway.
When traveling in general, probably best to wear/have one nice watch. Like you said, when you buy the Omega and wear it out immediately, it's best to conceal the Omega box and bag in a generic bag/backpack.
Enjoy your time here and your Seamaster purchase!