Use cut and (new) edge fades to white

[Ofnuts]

You can always use gimp-selection-sharpen() (which is the same as the Select>Sharpen menu). But IMHO your are misunderstanding something. The pixels on the edge of the polygon are partially transparent, but their RGB value is identical to the RGB values of the pixel in the polygon. The intermediate colors are due to this partial opacity blending with whatever is in the background. Normally you want to keep this partial opacity, this is what produces the smooth edges.