Paint.NET will do it, You just need to do a fill, with 'global' mode instead of contiguous mode.
As per request. I'd note the original was horribly noisy and I cleaned it up a bit. You'd ideally want to clean this up first
There's a few important things here.
Firstly, I was zoomed into the image so I could pick the correct area more easily. There was a ton of anti-aliasing here so I ended up sharpening it (or otherwise cleaning it up), but even then, I went with a fairly high tolerance (The higher the tolerance, the less similar an adjoining pixel needs to be to its neighbours to be recoloured) Play with that value - lower is more 'precise' but you may need a higher value.