Make a pizza without yeast or shortening?

Make a Pizza dough as you would normally make it with yeast. (Leave the yeast out)

Mix one teaspoon of baking powder into the flour before mixing it all together.

Add more flower to get the right consistency of the dough.

Bake immediately, do not wait for it to raise, as it wont raise without yeast anyway and waiting will decrease the efficiency of the baking powder.

When the dough get warm in the oven, the baking powder will release Co2 and make the dough nice and airy, much the same way as yeast does.

You might notice that the finished product will crumble easier than when you make dough with yeast.

(When I make pizza dough with baking powder I normally add 1 teaspoon per approx 250 grams of flour)