Interesting question, and not without its pitfalls. Shiny means reflecting which means bright so you need to boost the highlights. We often use a W shaped curve layer to create a metallic effect, so I guess you could try it on a furry animal. The pitfall I mentioned is that you are going to blow some of those highlights. Also not that the curves layer is set to Luminosity. If you get that radical with a curves layer set to Normal, your colours will go crazy!
A probably better way, and certainly more controlled, is to boost the highlights with the Dodge tool. It needs to be set to Highlights in the Options bar, and probably best to use a low value strength like the 10% I have here. Use a large fully soft brush, and build up the effect slowly trying to stop _just_ before you blow the highlights and lose detail.
Note that I used a copy of the original and set it to Luminosity again. I was just starting to see some of those light tan colours go a bit wierd on me. Another benefit of doing this is if you later decide you have gone to far you can add a layer mask to the layer you worked on, and with a low opacity brush (10%) mask out just enough to reveal detail from on the layer below. This is definitely the way that I would go about it.