My way may not be the best way, but what I did for a bow in similar condition was scrape off the fractured finish with a sharp straightedge. I then used 100 grit paper to smooth out the edges of the finish that had been left which was mainly at the fade-outs of the limbs as well as to refinish the riser. I followed this up with some 150 grit then 0000 steel wool before spraying on a new finish.
What kind of finish did you use?