Leather/paint on the wheel is comming off on my hands.
Is there any fix other than a new wheel ?

 

some of the after market sterring wheel covers they sell at car washes and auto stores are actually quiteattractive and provide a nice feel. its a $20 solution that may actually make your car look better.

 

run, fly to your saddle and tack store,
buy a bottle of BICK4 - sold at horse and saddle stores
and a bottle of PURE neatsfoot oil.

apply the BICK4 , follow it with the oil and hope for the best.
if it can be saved, this is the only way i know of.