I'm trying now to white an eye with Photoshop. I'm using
brush tool in Saturation mode. The color is perfect. But the veins becomes gray and they are pretty visible. I tried to remove them with healing tool but I'm getting to much mess.
Clone tool: brush the neighbouring pixels onto the veins. for horizontal veins use pixels under them, for verticals you the pixels to the side. making sure you dont brush on the edge of the eyes.
You can create a separate layer, smooth it and mask it onto the veins.
Here [left] clone [right] mask smooth
smooth is a bit unnatural unless you do a bit of layer transparency.
Use replace Color or selective color and make sure you set your History settings to allow non-linear history. Adjust to remove the red by lowering saturation and increasing luminance in the reds until your veins disappear. Surely you have now whacked the rest of the image, but no worries, just place the history brush on the current history state and back up to the prior state and brush in the correction.
Another approach: after reading about wavelet decomposition (in my case, using Gimp and plugins) I just loved the technique to do that kind of job.
Here's the result of a 50 sec. work, without worrying too much.
Depending on what you would use that zoomed picture for, I'd just paint with some white over it.
In general I never liked retouched photos that I paid some studio to do it. They all looked too plastic, too much blur to hide imperfections. Until recently I learnt about Wavelet decomposition in this blog.
I got the Gimp for Windows plugins here. The OP asked about Photoshop, googling around you can find some tutorials on how to do it (but don't know if they break the image in more than 2 layers: I decompose mine in 7, in general).
Seems that the Portraiture plugin for Photoshop does the same result, but don't know if you have the same control over your edition.
And yes, the spider veins are still there after the edition, just not too evident. When they are completely removed, the picture seems unnatural to me.