It doesn't make sense to cast one part. Most likely a good craftsman in brass could duplicate the part from brass sheet. If the design is such that it can't be made from sheet (has a big block in one spot, like the hinge, for instance) then it might be made in two pieces and joined. Experts in this type of fabrication can make hard solder joints you can't even see.
Guessing at what the part looks like, investment casting might be the only way to cast something long and thin, and such parts are often quite difficult.
I'm not sure what you mean by "casting set (punch & die?)". You cast molten metal in a mold, choices are such as sand casting, lost wax and investment. A punch and die would stamp a piece out of sheet metal. You can form the metal with a punch, too.
Jon