I have one that I push a trumpet mouth piece into to blow. Since I have been using a lathe for horns, I'd be tempted to turn a mouth piece from horn, using a trumpet mouth piece as a pattern. The trumpet tubing is 5/16" I think. I'll check on that. The mouth pieces have a slight taper on the end gong into the trumpet.
Some are very plain; others more ornate. A plain one would fit in best I think.
Regards,
Pletch