How to remove pizza pan from oven without a peel?
You can use a spatula or tongs to pull pizzas off of a pizza pan/stone in the oven onto an upside down baking sheet, cutting board, or even a plate, assuming your pans are just flat surfaces, like a pizza stone. 

You can also assemble pizzas on the upside down baking pan and slide them off it onto the stone in the oven.