In terms of what NYPD will act upon, you want your knife to be less than four inches in length, and carried completely concealed (no belt clip, no belt holster). A slipjoint (like your SAK) cannot be considered a "gravity knife" under the "wrist flick" "test".

I doubt that NYPD would get on your case, even as a non-US citizen, about a SAK kept in your pocket if you didn't try to get it past any magnetometer-type security.

The Empire State Building and The 9/11 Memorial have magnetometers. I'm almost 100% sure that The Statue of Liberty does as well. Last time I was in NYC neither the Museum of Natural History nor MOMA had magnetometers, but they do have staff who may choose to "randomly" wand you.

Last time I was in NYC I decided to pocket-carry a very small Spyderco non-locking "Slipit". It was inexpensive enough that I wouldn't have minded losing it very much, while still being very sharp and useful. It wasn't noticed.