For the head and claws I'd go for theatrical wig and beard hair suppliers (if I could go back in time to the early nineties I'd know just the place to get it too...darn).

The original puppet looks more like a shaggy misshaped human than a polar bear and the face is more hairy than furry, you might be able to massacre several out of season Santa wigs and beards, (a bit of spirit gum, morticians wax and razor blades can do wonders).

For the body, most of these suppliers are outside the UK but they might help.

http://www.andrewdavidson.com/links/faux-fur/

if it's horns you are after this might help too.

http://speyside-horn.co.uk/rawmaterial.html

They sell products made from horn but I'm sure if you contacted them they could get you some untouched samples.