Preheat oven to 350 degrees. Line two large cookie sheets with foil; set aside.
Drain tuna, reserving 1/4 cup of the liquid (if necessary, add some of the broth or milk to measure 1/4 cup.)
In a small bowl, combine tuna, the 1/4 cup reserved liquid, oil, and catnip.
In a medium bowl, stir together all-purpose flour and whole wheet flour. Stir in tuna mixture and cheese. If necessary, stir in up to 2 tablespoons water just until moistened. Form mixture into a ball.
On a lightly floured surface, roll dough into a 10-inch square. Using a pizza cutter or a knife, cut into 1/2-inch squares (bite-size for cats.) Place squares in a single layer on the prepared cookie sheets.
Bake on separate oven racks for 20 to 25 minutes or until light brown, rearranging cookie sheets halfwa through baking. Cool on cookie sheets on wire racks.
Storage: Place cat treats in an airtight container; cover. Store in the refrigerator for up to 1 week or freeze for up to 6 months.