I would think the first thing you should do is determine the value, maker, age, and real composition. If in fact that is real fur on skin and it has released due to age, then there is nothing to stop that. It would be due to the tanning process at the time. Remember, this was a child's toy meant for X number of years of use and not to last beyond that. If this is a Steiff bear, you may have a valuable item and any spot cleaning, combing, etc. would greatly diminish its value to a collector.
I would not clean your bear but set him on a shelf to look at and enjoy. Leave handling of him to an absolute minimum. JMO.