91 is legal. 121 you have to take the FFDO program and be sponsored by your air carrier. The nice thing about FFDO is you can get discounts on new firearms from SIG and Glock (prolly others as well). To conceal carry you cannot carry in a secure area of an airport meaning no Part 139 type airport, basically where paying pax are located. You could probably get away with conceal carry/open carry at smaller GA airports. I know some sea plane guys open carry down in Florida in case of run ins with gators. Same in Alaska wiht bears.
As always check local and state laws....Not sure with 135?