Earlier this year, I saw a (the?) Japanese version of the Butterfly stool in one of the department stores in Ginza. It is actually cheaper than the Vitra reproduction (~$350, IIRC). I.e. unless yours is more valuable than a current reproduction, I wouldn't go overboard with the restoration. One can't tell from the pictures what exactly needs to be fixed.

I think it looks great the way it is!

"Butterfly" stool (model no. T-0521), 1956
Sori Yanagi (Japanese, born 1915);
Manufacturer: Tendo Co. Ltd.
Rosewood, stainless steel; H. 15 1/4 in. (38.7 cm), W. 16 5/8 in. (42.4 cm), D. 12 in. (30.5 cm)

".. Ease of travel in the jet age encouraged a growing fusion of cultural influences after World War II. Although Yanagi's stool was designed and manufactured in Japan, it employs Western form (the stool) and material (bentwood). Its calligraphic elegance, however, suggests a distinctly Asian sensibility despite the rarity of such seating furniture in traditional Japanese culture. The stool is made from two curving and inverted L-shaped rosewood sections, each forming one leg and half of the seat. A metal rod midway between the legs serves as a stretcher and holds the stool together. .."

sweet, you got a pre-Vitra! don't risk messing it up with a botched resto'. all auction value will be lost if you change the finish in anyway, and that stained rosewood finish is notoriously tricky to get right.

- Supernormalist