How to remove green-eye in PP?

Photoshop Elements, which I use for PP, has a facility for removing red-eye from photos. However, it doesn't work on green-eye, which is what you get when you take a photo of a cat using flash. I'd appreciate some advice regaring the best way to handle this.

Here's an example of the problem, from my Greek cats gallery.

Byte size: ZERO | Content warning: NOT AN IMAGE

And here's a 100% crop from the original photo, showing the eyes:


I've tried using the various selection tools (primarily the Magic Wand) to select an appropriate part of the eye, which I can then alter. But I'm having a lot of trouble getting it to work properly. The reason is that there isn't a particularly hard edge to the green parts of the eyes: the colour blends gradually into the yellow iris of the eyes, so even working at 500% magnification it's hard to decide which pixels to select and which not to.

I feel sure there must be better ways of approaching this. Any suggestions?