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When I do a dog cake I usually do the fur with either an icing tip or candy clay. The icing bag will kill your hand really fast, and the candy clay takes longer, so there isn't a really good solution to how to make it.
I do think that the candy clay looks better than icing, though, so I prefer to use that.
When I use candy clay I usually use a clay gun, but the last time I needed to make hair for a dog cake I decided to try my garlic press. I think that it was a gift from Christmas a few years ago, but I've never used it (A chef's knife is much more effective for mashing garlic, as far as I'm concerned.)
This is by far the easiest way to make hair for an animal cake that I've found. The secret is the Zyliss 12040 Jumbo Garlic Press with Cleaner , which has a plastic plunger-type bar that presses the candy clay through on the inside, so nothing sticks to it.
It's really easy to press the clay through, and it cleans up with almost no effort.
I did a dog cake fairly quickly using the press, and my hand doesn't feel like I ran it through a wringer. If you're looking for a good tool that won't result in your hand looking like a claw, I'd definitely recommend this.