The only purpose that sidewall rubber has is to offer some protection to the cloth that makes up the actual tire casing. There are some tires (I'm thinking specifically of tubular track tires) that have no rubber at all on the sidewalls. In a pinch, I've ridden a recently-purchased bike 10 miles home on tires that have no sidewall rubber at all. If there is a crack or two in the sidewalls, you'll be fine. It doesn't affect the structural integrity of the tire at all.