Wood glue, ( white, PVA.) dilute abt %10 form when wet, but you can reform with heat, after drying .

I know mink oil softens leather allowing it to stretch.
I know that certain parts of the hide and certain species of animal are more well suited for certain applications.

Example Gun Holsters are best made from a part of the But hide where the leather is thick and tough. So too belting leather is from the but.

If you saturate leather with any glue that cures hard it will take on a hard stiffness but will also crack when bent.
It cracks because the fibers are bound up in the polymer and cannot flex, so fibers tear instead.

Maybe your masks should be composed of more than one type of leather is you want stiffness in some places and not in others.

Or you can add stiffening material ( like poly sheet material) to it and envelope the stiffeners into sewn-in pouches.