Combine flour and Greek yogurt in a large bowl. Dough will be crumble. Transfer to a lightly floured work surface and mix until it forms a ball. Knead until smooth, adding more flour as necessary to keep dough from sticking, about 3 minutes.
Divide dough into 4 equal pieces, and roll out each piece into a 4x7-inch rectangle about 4 1/8-inch thick.
Spread dough pieces with Dijon mustard and evenly top with Swiss cheese followed by ham slices, folded to fit. Pull up the long sides of the dough until they meet, and then pinch and seal. Tuck the ends under on the bottom, pinching and closing up dough pockets. Whisk together egg and water in a small bowl and brush egg wash onto the dough pockets.
Preheat the air fryer to 360 degrees F (180 degrees C) for 3 minutes. Lightly coat the air basket with cooking spray or line with a parchment liner.
Place dough pockets in the basket seam side down, being sure they're not touching.
Cook until golden brown, 9 to 10 minutes. You may have to work in batches depending on the size and brand of your air fryer. Transfer hot pockets to a wire rack, cool for 3 to 5 minutes, and serve hot.