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You could order a good-quality leather steering wheel sleeve (the kind that laces up) and carefully cut it to cover just the damaged sections while leaving the wooden portions of the steering wheel exposed. Check out the leather sleeves available from www.wheelskins.com.
Did mine with leather courant from Scratch Doctor . As I had an off white interior I did it in the same colour ...did not even take it off. very good result .brightened up the whole area
I did mine a couple of years ago. Purchased a cleaning and coloring set from Furniture Clinic in UK. Mine was Antelope AGE. Very good color match and still looks very good.
Any good auto paint store should be able to match the color using the code found in the left door jamb. What you want is usually called "vinyl dye", paint used for respraying vinyl & leather seat material.
HTH,