To the OP:
You said it's a work trip and that you are looking for supplies, correct?
I take this to mean that: 1. You have limited mobility, 2. You need stuff that can get through the "Blue Glove" treatment at the airport. Am I correct?
If you were visiting New Orleans and had access to a vehicle, I would tell you to take the 30-45 minute drive to LaPlace and visit
Jacob's and Bailey's.
I assume that you are limited to streetcars, cabs, and Uber's. If that is the case, get yourself to a Rouse's Market or Robert's (pronounced "row-bear", not "rob-ert"). Go to the seasoning section and look for Slap Ya' Mama, Punch Ya' Daddy, and other local seasonings.
If you are checking a bag at the airport, you can carry liquids. Look for Pig Stand and Johhny Miller's sauce. Also find a Winn Dixie and you can get the very excellent sauces made by Daigle's (pronounced "Day-gulls").
If you are really adventuresome, you can check frozen meats (no carry-on). Get a decent softsided cooler and fill it with crawfish tails, frozen shrimp, alligator meat, and some good cajun sausages (Manda's, Richard's ("Ree-chards"), Savoie's ("Sav-whaaz"), and others. Top the cooler with dry ice in a towel.
Visit Cochon Butcher and Chris' Specialty Meats.
If you are going out to eat, Blue Oak is pretty damn good.
If you are adventuresome, got to Toups Meatery.
If you want seafood, go to Mandina's, R&O's, or Blue Crab.
If you want boiled seafood, go to the Galley in Old Metairie.
If you want steaks, Crescent City Steakhouse or Mr. Johns.
Enjoy, and PM with any questions.
David