As it's is indeed made of cardboard, I don't think you'll be able to.
The best you can do, if you absolutely want it re-shaped, is opening up the mask at the oxygen inlet ring and put in a new piece.
Here's a pic I got of an original piece of cardboard. It came from an original mask that literally fell apart. You can clearly see it's cardboard:
Also: here's a pic of the hollow aluminum nose wires of that same mask: