Considering the shaft is case hardened steel, I would guess that anything short of replacing it would not be a reasonable repair. Is there visible wear to the splines? Is it the shaft or the sprocket that is worn? I have read (I think) that some sprocket brands move around more than other brands, what brand of sprocket do you have?
If there isn't any visible wear on either the sprocket or the shaft, then it probably isn't a problem and probably won't get any worse, but keep a sharp eye on it. If there is visible wear on the sprocket but not on the shaft, then replace the sprocket and see how it lasts. If there is visible wear on the shaft, watch it until it fails, then replace the shaft.
It's my guess that the slop is inherent and the shaft won't wear out before the sprocket does.