Then I have good news for you: that is not what the NYC mandate says. Here are the businesses you need to show vaccination proof to patronize or work at.
Indoor dining
Includes restaurants, catering halls, event spaces, hotel banquet rooms, bars, nightclubs, cafeterias, grocery stores with indoor dining, coffee shops and fast food or quick service with indoor dining
Indoor fitness
Includes gyms, fitness centers, fitness classes, pools, indoor studios and dance studios
Indoor entertainment
Includes movie theaters, music and concert venues, museums, aquariums and zoos, professional sports arenas, indoor stadiums, convention centers, exhibition halls, performing arts theaters, bowling alleys, arcades, pool and billiard halls, recreational game centers, adult entertainment and indoor play areas