Grate both cheeses with a rotary cheese grater, the fine holes of a box grater, or the fine shredding disk in the food processor. In a food processor fitted with a steel blade or with a mixer, cream the cheeses and butter until fluffy and smooth.
Add the cayenne, salt, and flour and process or work it in until the dough is smooth. Gather it into a ball, wrap well in plastic wrap, and chill for at least half an hour or up to 1 hour, but don’t let it get completely hard. If you make it ahead to bake later, let it soften at room temperature for about half an hour, so that it’s still cool but pliable.
Position a rack in the center of the oven and preheat the oven to 325° F. Put the dough in a cookie press fitted with the star die and press it out onto an un-greased baking sheet into narrow 2-1/2-inch straws, leaving about half an inch clear between. If you don’t have a press, lightly flour a work surface and roll the dough out ¼ inch thick. Cut it with a sharp knife or a zigzag pastry wheel into 1/2-inch by 2-1/2-inch strips, laying them on the buttered baking sheet as you go. Or for a more decorative straw without the cookie press, roll them out a little thicker than 1/8-inch and cut into decorative shapes with small (bite-size) cookie cutters.
Bake for about 18 to 20 minutes, being careful not to let them brown on top. Cool on the pan before transferring them to an airtight storage container.