I would start with a plastic mask base so that you have something to build off of, but you could also make a base to work off of. Then I would use a lightweight clay like foam clay or paper clay to build up the details. I think sculpting is a great way to achieve those organic shapes and gives you a lot of freedom to change and adjust as you build or sand down dried areas.
If you’re not big on sculpting, then you could use craft foam/EVA foam to build the mask. Cutting craft foam gives you a lot of control over the less organic shapes. Thicker sheets of EVA foam can be sanded with a dremel tool to sculpt the curves of the mask and create the more organic shapes.
Even though foam and paper clay are pretty lightweight materials, the mask may be a bit heavy to support with a basic string. I would use a strap that goes around the back of the head and one that goes over the top of the head and connects in the back. This will be covered by the fur, so you can make the straps as thick as you need for support. Alternatively, make the fur into a sort of hat that is secure on your head and then attach the mask to the fur-hat.