As it was the scenario during World War 1 the lack of raw materials during World War 2 was extensive. Firstly the war lead to a decreasing production of bears due to the change of tasks the production was forced to undergo and secondly that the bears that were manufactured were made of cheaper materials such as 'Sub' - a textile industrial-waste product - used as filling and pads which were made of e.g. "a painted wowen fabric also called leathercloth"rexine.
Rationing continued after the war which once again caused new materials: fabrics such as e.g. nylon and rayon and muzzles were occasionally made of vinyl, plastic or rubber. In 1955 the first 100 % washable teddy bear was manufactured by Wendy Boston. You could in fact put it in your washing machine as a result of the way the eyes had been mounted and because the kapok-filling had been replaced by rubber-foam.
Anyway not all teddies were manufactured with all of those new materials, the old companies mostly honoured the traditions and as far as the raw materials allowed they proceeded to use traditionel materials.
After the war quite a few new German and Austrian companies were established e.g. Clemens, berg and Fechter and in USA Gund began with exclusive rights to produce Walt Disney toys and bears.